Tables de sinus, tangentes, et secantes, et de logarithmes des sinus, tangentes, et des nombres ...

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i

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C}i

TABLE S

DE S I N U S >

TANGENTES»

ET SECANT E^S,

E T D E

LOGARITHMES

DES SINUS, TANGENTES,

Et des Nombres depuis l'unité
ju{c]^ues à looob.

A'vec une Méthode pour refondre tres-faci-
lement par leur moyen tous les Triantes
Reéiilignes & Spheriques , & plufieurs
^ueJHons AjirQnomiques.

Par A^V L AC Q.

Dernière Edition , corrigée & augmentée.

A PARIS,
Chez Jean Jombert, prés des Auguftins,
i l'Image Nâcrc-Dame.

M D- C I C.
ÂFEC PRirilEGE DV ROT.

/

■ N

CHAPITRE PREMIER.

DE WSAGE VB CES TABLES.

CE traité contient une double 4iftinâion df
tables t £n la première y celle des Sinus , Tan^
t Rentes , & Sécantes > de chaque degré Se minute du
;;^ quart de Cercle , dont le demi • diamètre cft de
^jnoooôôoo parties : enlèmble let Logarithmes d^
j^ Sinus Se Tangentes , obmettaht expreflement ceux
^ des Sécantes , parce que fans lés Sécantes les calculs
r de la Trigonométrie ie font de pateille fkdKté. £b
ry l'autre 5 celle des Logarithmes pour les nombres ab-
\ Iblus depuis lunité jufques i toooo.
^ On peut pat le nàoyen de ces tables refbûdrre tout
^ triangle en deuk manières » fçavoit parles notnbres
Vulgaires des Sinus > Tangentes > Se Secaktts > ou pat
leurs Logarithmes.

En la Règle de trois , ta diSêrem^e du calcul trigoH
hômetrique par nombres vulgaire&>& pat Logarithmes>
tft tellci

Voulant calculer par nombres vuleaitës » il faut mul-
tiplier le fécond nombre parlé troiuéme , Se divifer le
produit par le premier 2 le quotient fêta le quatrième.
Mais , (i on veut calculer par leurs Logarithmes >
il faut ajouter le Logarithme du fetondavec le Loga^
tithme du troifiéme , Se ôter de la fomme le Logaricb-
me du pretnier: le nôtnbte reftaurferalelogarithose
du quatrième , lequel étant cherché dans la première
ou dans la dérniete Table ( félon qu'en fèta la nanite)
donnera le quatrième requis. ^

Cette manière eft beaucoup plus facile que l'autre »
princip^cment aux refolutiods de tous les Triangles
Spheriques > car aux scfoluciori» de plttikuts Trian^tt. ^

'4 ChAV. h De Vufage de ces Tailes.
leâilieties» coitimede la 3. 4. (?• Prop. &c. ileftp!as
aisé d ufer de l'autre manière, ce que je laKTe à la àiù
cretion des calculeurs.

Or daucaut que la dernière Table contient feule-
ment les Logarithmes des nombres depuis l'unité juf-
qucs à looop , je montreray comment on pourra trou-
ver le Logarithme d*un nombre qui fera entre loooo
€c 10060000 , fie au contraire.

1. Chercl\ez dans la dernière Table. le Logarith-
itic des quatre premières figures du nombre donné.

2. Otez le Logarithme trouvé du Logarithme im*
mediatement fuivant eh la Table , pour avoir leur
différence;

f. Multipliez la différence trouvée , par les figures
xeftantes du nombre donné) 5c coupez du produit vers
h main droite autant de figures qu'il en fera rcfté^

4. Ajoutez le refte du produit au Logarithme. pre-
.mierénicnt trouvé , la fomme fera le Logarithme re-
quis , fi l'on change la première figure , qui doit tou^
jours être moitidre d'une unité que le nombre des fi«>
gures , dont le nombre entier donné coniîflc.
' Exemple. Qu'il faille' trouver le Logarichine de
35^7^9^* Premièrement je trouve le Logarithme de
35/Î7 , qui efl 3. 552.3031 : lequel étant ôté de 3. 55241489
•la ckffcrence fe trobve iitj , laquelle étant multipliée
par S94 ( les trois figures refiantes ^ } le produit dk
1087998 » dont trois figures étans coupées y il refte
,1087, qui étans ajoutez auLogarithme3. 55130,^1, la
(bmme efl3 5524118 Enfin la première figure3. étant
changée' eh ^ , le Logarithme du nom1)re donné
'35^7'94 cfl <>i 5514118. . . ]

Ainfi le Logarithme de ii^6oy t(ï y 0990157: &C
de 1358009 le Logarithme cfl: 6. jji^^^^.
Remarque.

Etant donné, le nombre ir^^ : ou z^SL^l^i ou

35$^^~ ,&c. leurs Loganthmes font les mêmes quecc-

Ju^ du nombre entier ^5(77894 , horfmis la première

CnAV. !• De Vnfage de ces TaHeu 5

figure, (çavoir o. 5514118 : i. 55x4118. 2. 5524118, &c«
& pour les troviver il n'y a aucune difFcrence.

Et fi un nombre entier avec une fraftion décima-
le, n'ayant en tout plus de 4 figures, eft donné, on
trouvera (pn Logarithme cxaftemenc dans la mèmfc
Table. Comme de 3-^£-, ou l^-^^.oxi 35677 > les Lo-
garithmes fe trouvent vis à vis le nombre entier 3567-,
en changeant feulement la première figure , comme
il a été dit cy-deflus.

Mais fi une autre efpcce de fradion eft jointe a un
inombre entier, reduifez ce nombre-là àunefradtion
impropre , & ôtcz le Logarithme du Dénominateur
du Logarithme du Numérateur , le refte eft le Loga-
rithme requis.

Comme 3I étant réduit,il vient, -|-, donc o. <302c(^oo
( le Logarithme de 4) étant ôté de u 17^0913 (le Lo-
garithme de 15 , ) le refte o. 574031} eft le Logarithme
•^« 3| ou 3^.

* Vous voyesJ donc icy que les fr,aéî;ipns décimales,
tant en Tufagc des Logarithmes qu'en l'ufage des nom-
bres vulgaires , donnent une grande facilité : & par-
taqt ^ous les recommandons pardeflus tous les autres*

Pour trouver le Logarithme d'un nombre rompu ,
il faut ôter le Logarithme du Numérateur du Loga-
rithme du Dénominateur, le refte eft le Logarithme
«quis , en luy ajoutant la marque - , qui fignifie moins.
^ Mais ,^ il faut ^fçavoir qu'on doit opérer autrement
par Logarithmes des Nombres rompus que par Loga-
rithmes des Nombres entiers , ou d'entiers avec fra-
«âions > œ^ que nous n'enfeignerons pas. icy , parce
que rarement ils viennent en ilfaige dans les refolu-
tions des Triangles. Ceux qui le défirent fçavoir , le
pourront apprendre en l'' Arithmétique Logarithmeti-
que d'Henry Briggs yQVi le fondement & l'excellent
ufage des Logarithmes aux qiieftions Arithmétiques
^ Géométriques font am|>lement déclarez^

Ai»

$ Chàp. I. Z)^ Vufa^edi cês TaJkUu

Trouver le nombre à* nit Logarithme donné. i

Cherchez en la deÂiicrc Table entre les Logarick-
mes de iQoo & 10000 , ( ians avoic égard à Taprc^
miere figure ,J le Logarithme donné , & re^iarque?
^C5 deux choies.

Premièrement, fi vous trouve» ex^ftement le Lo-
garichme donné , vous y avez vis à vis le nombre re«
quis ; Et fi la première figure du Logarithme donne
eft moindre que 5 , coupez du nombre trouyé vers I4
droite autant défigures quelle tft moindre , le reftc
fera le nqmbre entier requis , & les figures coupées
feront des fraâions décimales. Mais , h la première
figure efl plus grande que j , augmente* le nombre
trouvé d'autant de zéro qu elle cft plus grande. Ainû
\t Logarithme 3. 55130}! étant proppfé , fon nombre
fera ^6jx fi %. 5515051, fon Nombre fera i^û-^iQ.
ï.55Zjojt , fon nombre fera )St|^> fi o. 55i50}x foa
nombre fera 7^; fi 4. 55150}!, fon nombre fera
15(^70: fi' 5. j5i}o3i » fon nombre fera jjiîyoo. Ainfi
des autres.

Secondement y fi on ne trouve pas exa<P:ttiient le
Logarithme donné , & qu'on demande plus de qua«
tre figures , faites ainfi.

I. Cherchez comme auparavant , fans avoir égard
à la première figure , le Logarithme prochainement
moindre que le donne , & prenez le nombre répon-?
dant au Logarithnae trouvé poiu: les quatre premières
figures du nombre requis.

z. Otez le Logarithme t?rouvé du Logarithme don-*
t)é , & augmentez le refte dHm, deux, ou trois zéro ^
félon le nombre des figures que vous demanderez qut
|re les quatre trouvées.

}. Divifcz ce refte ainfi augmenté par la dififerençç
entre le Logarithme trouvé & celuy qui le fuit inv-
mediatement , & mettez le quotient vers la droite
des quatre trouvées, Cela &it , regardez la première

C H A p. I. Vo Vftfageâc ce$ TaliUs^. jr
fipmbce entier & la &aâ:ion du nombre trouvé , cptnr
fne nous avons dit auparavant*

Exemple. Qu'il faille trouver le npmbre répondant
âu Logarithme donné 4, 55x4118.

Le Logarithme qui fe trouve en la Table entre
ceux de 1000, Se ioooo> fans avoir égard ila prer
xniere figure , approchant le plus prés & moindre que
le donné, eA |. 552;o;i » duquel le nombre çft }5<^7,
qui (ont les quatre premières figures du nombre re-
ijuis. Or ce Logarithme trouvé étant pté du donné >
le refte cft 10S7 , que vous augmenterez de trois zcroj
pour avoir 1087000, Divifez ^ ecy par 1^17 » la ditfc-
içnce entre le Logarithme trouvé & le fuivam» Iç
quotient cft 894 : mettez ces figures après 3567 » 6ç
vous aurez le nombre ;5^78$4* Or puifque la pre-
mière figure du Logarithme donné eft 4 > le nombre
cequis cft 35^787!^ •

Trouver U Racine ^^Marr^e êu Cubique d'un.
nombre donné.

Bien quemon intention ne (bit que de brièvement
décrire en ce lieu la manière de>fupputec les Trian-
gles : Toutcsfois puifque Tufage des Logarithmes cft
admirable aux extrairions de Racines Carrées > Cu-
bique*, &c. j'ay trouvé bon d'y ajouter en peu de
irgnes , comment on les peut tres-facilemcnt cxtrairç.
four avoir la racine quarrée d*un nombre donné y fn^

nez* la moitié du Logarithme du nombre donné ^

UqneUe fera le Logarithme de U r4cim qnarrée

quon demande.

Comme fi on demande la Racine quarrée de U57 :
Ion Logarithme cft j, 05)93355, &b moitié 1.549^67$,
qui eft le Logarithme de 35-^^ la Racine Quarrécrô-
quife.
pour trouver la Racine Cubique ttun nombre proposé ,

le tiers du Logarithme du nombre donné fera le

Logarithme de lafiacine Cubique qu*on demanda.

Par exemple on demande Ja Racine Cubique ^c

s Ch.Ap. I. DeTnfagc de ces 'fahles:
Ï2570. Son Logarithme eft 4. 0993355 , & fc tiers
i. 3^<>445i , .qui eft le Logarithme de i^-^ la Racine
Cubique rcquife.
De la ndtHre,cr de U atnfiruWen des Logarithmes. ^
Les Logarithmes font des nombres pris à difcre-
tion » lefquels étans joints ou corrcfpondans à des
nombres Géométriquement proportionels retiennent
toujours entte eux des différences égales , ou bien
qui girdcnt la progreffion Arithmétique , tandis que
ceux defquels ils font dits Logarithmes , çonferveat
ta Géométrique.

Voyez la premicre colomne de-
cette Table, ou (ont les nombres Géo-
métriquement proportionels , auf-'
quels il repond vis à vis dans les aiu
1res coldmnes leurs Logarithtties , qui
pciivejQt eftce pris à dilcretion , com-
me vous voyez, ctâni Ubre de pofcr
ce que, Ton veut pour premier Loga-
nrîthme , & pour leur différence proy
greffive. Mais , ayant détermine le
logarithme de deux nombres , il n'eft

Îlus libre d'en déterminer d'autres.-
ar exemple le Logarithme de l'unité étant i , & rfe 2, ,
•étant 2 , le Logarithme de 4 fera par ncceffitc j 5 & 4

fera le Logarithme de 8. Que fi le Logarithme de Tti-
'nitc eft j , &le Logarithme de 2 eft 5 , le Logarithme

de 4 fera ncccffaircment 7, & y fera le Logarithme

de 8, ,Aiafi des autres. . .
" " Or Jâ propriété des Logarithmes eft telle ^ qiio
• quand qtiatre nombres font piroportionels 5 la fom-
"me dcletïrs Loearithmës extrêmes eft égale âlafom*

jme des Lpgarithmes moyens.
\- Exemple. Comme x eft â8, ainfi \é eft a ^4 U

fomme du Logarithme dé 2, & du Logarithme de

64 , fera égale à la fomme des Logarithmes de 8. 5c
'de 16. ' . -

tro-

L9gMriih

port.

mes.

I

I

a

. X

z

10.

- 4

5

10

%

4

io

J6

5

40

Ji

6

50

^4

7

60

1x8

a

70

156

9

80

/li

10

^0

1014

II

100

Chàp. I. De Tufage de cesTabîesZ 9

D*où il fait qu'au lieu de faite la Règle de trois
car mulciplicarion & par divifion , pour trouver com-
«ne a l'ordinaire le quatrième noipbre proportionnel »
il oh'ajoûteles Logarithmes des moyens, &que de
teur fommc on ôte le Logarithme du premier , il re-
liera le Logarithme du quatrième requis » à côt^ du-
<5ucl on trouvera ce quatrième nombre.

Et partant il n'y a qu'à faire éts Tables des Lo-
garithmes cotrefpondans à tous les nombres naturels >
comme je montreray cy-aprés. Je dis correfpondans
depuis Tunité confecutivement fans laiflTer de vuide ,
comme il y a entre les nombres cy-deflus propor-
tionels 4. 8. i(i.&c. où les nombres 3. 5. 7. ^•&d
manquent , qui pourtant doivent avoir leurs Logarith-
mes, parce qu'on en peut avoir befoin. C'cft pour-
quoy, il faut faire la diflfercnce de* ces Logarithmes
fi grande , qu'on puifle aisémeiic aflignet a chaque
nombre Ton Logarithme » fans
que les &aâions en puifTenc être
fenfibleis , comme il fera dit.

Pour cette 6n l'on a fuppofé

pour plus grande facilite que le

5. 0000000 j Logarithme de i.fut o. & que le

4.oQooooo| j^^ j^j^j^ç de 10 fut 1.0000000,

f.oooooopi o , . , j - '

^.0000000 .q^ic le Logarithme de 100 ftit
7.0000000 i.ooooooo, que celuy de 1000
8.0006000 Ifuf 3.0600000, & ainfienfiiite.

Prop.

Lêgarith^
mes.

I

10

ipo

1000

lOOOO

lOOOOO

I 000000

I 0000000

I 00000000

0.0000000
1 .0000000
1. 0000000;

comme vous voyez en cette Table, Où il eft à rc-
marque^r que la première figure du Logarithme , nom-
mée c^dinaircmcnt CaraEierifiique , eft toujours moin*
die^d'une unité que les ifigurcs dont le nombre natu«
rcl eft compofé. Si par exemple il eft de S chif&es »
la première figure de fbn Logarithme fera 7. Si de ii
chiffres , fon Logarithme aura^ 11 pour CaraOerifii^

Et fur ce pied & fondement on a trouve les Lo-
gariihipcç de tous les nombres, même, de ceux qui

^t4ei9>iO><leipâioP9ckioo âiooo, &c âbnt
pîi a drclTE des Tables > fi bien qu au lieu d opérer
par timtciplicatiop & par divifiou pour trouver le 4»
jBQipbre requis , fi Ion opère par Addition & par
$oil^ra£Hon des Logarithmes qui répondent aux uois
iioi:9t>res donnez > on aura le Logarithme do 4. tt^
quisy dcôté duquel il fe trouvera en la colomne det
jDofnbres naturels.

Et doutant qu'avec les Tables des Sinus te des
Ts^^ntes y comme étans des ao^ibrcs naturels » il
laut Qperer pv muldplication & par divifion > on a
wflî cherché \t% Logatithmef de tous ces nombres
^ Sinus le Tangentes k Tég^d du Sinus total
locpooooooo , auquel on applique pour fon Logarith-
me lo.oocooop » & tous ies autres k proportion , que
Ton a fubftituéen la place d^% Sinus & desTangeiw
tfft ordinaires.

Pe façon qu au lieu de les multiplier & delesdi*
Yii^ s'ils y éa>ienc , on ne fait qu'ajouter & fouftrai-^
re leurs Logarithmes ^ pour avoir le 4. requis , à coté
duquel on trouver le degré Çc minute , comme fi c'é-
|o>t le Sinus ou^Ia Tangente m&me > puisqu'ils font
iubftituez en leur place.

PoHr tr^mjer h Ij9gêrUbme d'un nombre donné
quel qH'ilfin , comme pdr exemple de 9 , nui efi entre
jt tà' i^ > dont les Logarithmes font dé je donne^yffd^

voir o.ooooooQ, ^ i. ooooopQ, ou tien 0.00000000»

0' !• ©oooçoop , en les augmentant d'un 7(ero , four

trouver plus exdSemtnt le Logarithme f faites en

cette forte.

Entre » & 10 augn^entesç

d^âutanç de ^eiro que le Lo^-

garirhme de lo & des au-

frcs proportionnels % ^pm-

mc icy de fcpr j pour avoir

l^xaAenient dans le même

nombre de figures le Lo-

f report. \ LogMtth.

1 .oooocpo jo.ooooooco

3.1^1x777 jo.jooooooo

I o.coôoooo 1 1 .00000000

►oji

1 0.0060000 i I^OOCOOOOO
j.6i34i|i|o.7joooooo
5 . 1 <;iz777 lo./ODOooo©

Chaf. ï. JieVnfuge
earithtne requis , fçavoir cp-
tre les nombres A » B , ti ou-
vez un moyen Géométrique
proportionnel C ; lequel é-
uc moindre que 9.0000000,
il faudra chercher encre le
nioindre C , & le pins grand
jB un autre moyen propoi:*
cionnel D , qui eft encore
înoindre que 9. oeooôQp ,
ç'eft pourquoy entre le
fnoindre D & le plus grand ---^
B on cherchera un autre
inoyen proportionnel E > en-
tre lequel & le plus grand
B on trouvera un quatcié-
ine moyen proportionnel F
qui eft icy encore moindre
que 9.0000000 9 c'eft pour
quoy il faudra trouver entre
Je moindre F , & le plus
grand B , un dnquicme
moyen proportionnel G, qui
fera icy plus grand que
9. 0000000, ainfi entre le
plus grand G , & le prochai-
nement moindre F , on cher
cher^ un fîxiéme moyen
proportionnel H » qui fera
maintenant moindre quç
9, 0000000: c^eftpourqupy
çnae ce moindre H> ii le
prochainement plus grand
G, oin trouvera un feptiéme
ipioycn proportionnel (, qui
eft bien plus grand que
jp. QçoQooo , |!na|s nop pw

JéCf^Tahlcf^.

G
H
F

"g

I
H

T
K

H

1k

L
H

L
M

H

L

N
M

N
O
M

O

P

IM

Pr$fart.

lo.ooopooo

7.458^411

lo.ooooopo
70^f4*ï

10.0000000
^.jo/7104

8.^j^tf45i
^.}o;7i04

J?.JPJ7104
5.13^8170

8.57^8713

^.X55«i70
'9'0S79777
8.^7^8713

9'0S79777
5.0I7J333

8.^7^8713

90173$}$
^-9970796
8-57^8713

5>.oi73333
^.0071008
i'997079^

^.0071008
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Z.997079^

^.0011388
8.9^5^088
8 9^970796

LâgWt.

1. 00000000
o.tt7/ocooo
0.7/000000

1 .00000000
0-^37/0000
0.87/00000

1 .00000000
0.^^87/000
0-^37/0000

0.^^87/000
0.^/311/00
o-^J 7/0000

0.^687/000
o.^éo^37/o
o.^3^ift/oo

0.^^0557/0
0.5/70311/

0.5/3 Il/OQ

0.5/70311/

0.5//07811
0.5/3I1/OQ

o.5/;o78ii
o.5/4ioi/<î
0.5/3 ii/oç

0.5//07811

0.5/4/8584
0.5/4101/^

0.5/4/8584^
0.5/434/70
0.5/4101/6

0.5/4)4/70

0.5/4113^3
05/4101/6

[ Vrafort,

^.0011588
5.00087J7
8.^5^5^088

5.0008757
5.0C014XZ

5-000141 ^
^'9999tSO
8.555^088

5.0001412
5.0000851
^9999iSO

5.0000851
5.0000041
S.9999^SO

il CnxvA. De fufage de ces Tahles.
avec an fi grand exçcz com-
me le précèdent G. Ainfi
en cherchant entre le pro-
chainement moindre & le
prochainement plus grand ,
des moyens Géométriques
proportionnels , on aura àzs
nombres qui approcheront
toujours de plus en plus du
nombre propofé 9.0000000,
lequel enfin fe renconttera
icy le x6> moyen proportion-
nel : Après quoy il fera fe-
cile de venir à la connoiflan-
ce de (on Logarithme; car
comme entre les nombres
A , B , nous avons trouvé un
inoyen Géométrique pro-

Ïonionnel C » (i ent^e leurs
►ogarithmcs on trouve un
moyen Arithmétique pro-
portionnel , ccluy-cy fera le
Logarithme du premier
moyen Géométrique pro
portionncl C. Ceft de cette
manière qu'on trouvera les
Logarithmes de tous les au-
tres moyens Géométriques
proportionnels , & par
comcqucnt du dernier
9. 0000000 9 ou du nom-
bre pioposé 9 , (Ravoir
o. 9y^i^i$o.

On ne trouvera pas au-
tr îment les Logarithmes desj bB
D >mbres premiers , & pàrl&
l'addition de leurs Logarith-

o

Q.

p

a

R
P

R
S

P

R
T
S

T
V
J

V
X

s

V
Y
X

V
Z

Y

V
Se
Z

V

AA

&

AA

50000041
^'9999^10
^'9999^5^

5.0000041

8.5^5584;
^'99996S0

5.0000041
^-99999^}
^'9999^^5

Logartf.

<"-^/434;70
0.5/4184^7
o.5;4î'iî^3

0.5/418467
0.5/41/41/
0.5/4123^3

0.5/41/41/
0.5/413885
0.5/411363

0.5/41/41/^
0.5/4146/1
0.5/413885

0.5/4146/ 1
0.5/41417»
0.5/413885

0.5/41417Ï
0.5/414080

0.5/413885

0.51414171

0.5/414117
0,5/414080

0.5/42417Ï
0.5/414113
0.5/414117

5.0000041
%.999999^
^'99999^1

5.0000041
5.OcrO00lé

%.999999^

5.0000016
5.0000004
8.5599^^1

0.5/414171
0.5/414147
0.5/414111

0.5/414171
0.5/4141/5

0.5/414147

0.8/4141/5^
0.5/4141/3
0.5/414147

C il îK. 1 1 Des Tritmgh nttH. nBan^.
tncs on aura facilement les—

n

BB

GC

&

BB
1>Ï>

Profort. \ Log^rk,

10.5

5.1000004 10.^/4 141/ 3

^'999999^
%.999999t

5.0000004
5.0000000
Z.999999^

0.5/4141JÛ
o.9S^HM7

Logarithmes des autreis nô-

bres > ce qui eft fi évident

par ce que nous avons die

cy-delTus , que ) ay honte

d'en padtc davantage. Je

fçay Dien pluâeurs autres

Méthodes pour rinvention\ £S

des Logarithmes , mais je n'en ^ay point de plui

prompte que celle-cy.

0^/4143^/5
0.5/414»/!
0.5/4141/0

CH AP ITRÈ IL

Du CaIchI des Triangles nâtlignes refhingles*

Ôb sbryations.

t. *rx Es Triangles reâangles , tanc reétilignes qde
JLx Spheriqiles , les cotez comprenans Tangle
droit font appeliez jambes , & le côté qui luy eft
oppofc, hj/fotenufe.

2. De tout Triangle tant reftiliene que Sphetique,
le plus grand angle eft.foûtenu du plus grand coti»
Et le plus grand côté foûtient le plus grand angle.

3. De tout Triangle reéliligne les trois angles pris
cnfemble font égaux à deux droits.

. 4* Aux proportions fuivàntes eeneralementnoils
avons obfervé un tel ordre» que les premières (ont
pour trouver les Angles , & les dernières pour'leç
cotez. Et de ccux-cy aux Triangles te ftangles, prc*-
mierement les jambes, 6c puis après Thypotenufe.

5. Les termes connus, tant angles que cotez , ,fe-
iront marquez d'une petite ligne, & les termes requis j
ii un petit cercle, ou , comme Ton peut voir icy.

'ig Ça A p. IL I)esTria9^.rc£Ht.reii4n£h

y L P R o Pr Lîûti^ connus les angles , & Une jambe v
trouver rhypotenufc.

Comme J^ Sinus total , V ^ /

ui ia jamhe\ conntu ; \ ( connue ,

jiinfila Sécante de V angle aigu adjacent f la jambe
A rhypotenHfe.

Si quelqu'un veut concoure le Logarithme de la
Sécante d'un arc , on le trouvera eh ôcant le Loea«
rithme du Sinus de Ton complément , du Logarithme
doublé du Sinus total : le ^efte fera le Logarithme re-
quis. . . -

Ainfi étant 9. 9445811 le Logarithme du Sinus de
Çi 'd..46. dç 2^0.' 0000000 i il irefte 10. 0554173 U Loga-*'
lichme de U Sécante de iSjd.iô.

Autrement éias Sécantes.
% . • .■ t. - . . . ' ■ '

Comme le Sint^ ieVangU. offoséà la jambe connue t
" ui la Jamb'i connue : .

'Ainfi le Sinus total,

A Vhjfotenufé. ' ^ ' -

V I L P R o p. Etans connues les jambes 9 trouves

l'hypotenufc. . .
I . - - -

09erchex» premièrement les angles par la u Prop. cJ*
fuis après ihjpotenufef par la précédente C. Prop. ' -

CHAPITRE IIL

De la fiippuiation des^ Triangles reElilignes
' " obliquangles.

L Pjlop. TjTans connus deux cotez , &un angle op-
JlI pps^ i l'un des deux , trouver l'angle op-
posé a l'autre : Moyennant quonffache s'il eft aigu oh
obtus* * . Comm9

^ k À p. 1 1 1. Des Triangl. rtttiU phli^^ ij
^ C^mme le cité êffùsé à l'angU connu i
ji$$ SinHs du même éngte i
Jlinfi l'autre cité 9 \

Au Sinus de tungte opfosi l ce citi.

ÏU JP R o i^. Ecanifi connus deux totex , & rahdê qû'ill
comprenaent » trouvée les autres angles;

Comme lafimmo des cêtex, connus ,

A la différence dis mêmes côtel ; ; '
Ainfi la Tangente delà moitié de la fimme disan-^
gies inconnâs ,
A la "tangente de la moitié de ledr différencia
Partant (i à la moitié des angles inconnus » qui (ont
le complément de l'angle connu ï i8o degrez , la dif-
férence trouvée éft ajoutée > la fditinie Teira le plusf
grand angle > & fi tlle en eft 6tée i le tefte fera le
xrioindf e ângic;

It 1. 1* id p^ Etaiis cbntiui lei tft>is ràtez » trduvef
quelcp'un des angles.

Prêtiez le plus girahd coté|>our la bafe , far laquîclA.
le tômbç de Van^é'>çpposé une perpendiculaire > ré-^
duifaat le Triangle fen deux Triangles itOaA^ési.
Alors on dira i"^ '

tomme la Bafi ,
- - A la fomme des autres chez, i

Ainfi ta différend des tèêmes cttei ,
/ A la diffeiren ce des deuxfigmehs de la tdfe^

la différence trpuvée étaiit ôtée de la bafe » ta pef-'
pèndiculaire divife le fefte en deui p'arties égalés;
Ainfi donc aux deux 'triangles reâangîes rEypote-^
nufe eft connue atec une ïambe , par lerqùellcs on
treuve les angles par la IL Prdp. dû CKap. II.

i8 C H A p. n i. Hes trrangi rcBit. eiUf.

Exemple. Au triangle obli-

quanglcÂBC, fontcoti»-

nus AC 1177, AB 8^5 g

& BC 6ji : on deman->

.de quclqaun des angles.

Comme A C

iABtBC
ÂinfiAB-BC

1177 --
145)7 -«

Logarithmes.

- 5. 1061909

- 5.1751118

5-3445777

- i-4î^J^68

 AD 17^

REMARQUE.

> Vj-

0» fei$l: 0i»gi trouver le Logarithme dn quMriinii
mnésev requis ^ file câmplen^ne ^rithnctiijue ^ufre-^
mier Logarithme , que Von a en Votant de 10. oQpçc^oô,
efi" ajouté aux deux autres , & que de iafomme on
60f 'Vtrf . iug4fH^ :h fr€mkr< /sf^.^\ C^^^^.^f^
VexemfU précédante ■;•
Logarithmes,
AC I277ii,h3^i

ABtBC I4p7-Î'ï7i5i«i8
AB-BC A5r.i>3g 7?559

AD 273- 12-45^3868 - - -

5i un Logarithme propcfé né peut pas êtrefonftrait
de To. 0000060 , comme ceux des Tangentes des arcs
outre J^^ degrez, , il le faut fonfiraircde io.ooôoooo ^
t^ faire comme devant, jiinfi le complément Arith^
nutique du Logarithme de la Tangente de 66 degrez. ,
1^ 9. 6 4 8 5 8 5 1 , qui efi aujji le Logarithme delà Tan-
gente de fin complément*

Or AD 17} étant ôté de A C l'i 7 7 , il demeure
D C 1004 % dont la moitié 501 eft C E ou E D. Main-

tenant au Triangle reâangle A B E eft connue l'hy?-
i>otenafe A B 8 6 5 , & la j^mbe A E 775 > par lefqueù-
Ics on trouvera l'angle A B E «^3 d: 38 & Tanglc
B A E 2(î d: ti\ De même au Tnandexcâangle C B E^
cft Thypotenufc G B *ji , & la jambe C E 502 , par lef-
qucllcs on trouvera Tapgle C BE 5^ d: 35'. ftianglf
B G E 37 d: 15'. Si vous ajoûtci l'angle CBE ci d: 3$';
à l'angle A B E £3 d: 38'. la fdnime eft l'angle A B â
ii^diy'.

ÂutHemènt.

Ajoutez énfi:fnt)le les trois cotez» & de la moitié
de leur fbmmé {buftrayez chaque côté comprenant
l'angle requis , pour avoir Icûts différences. Apréâ
tela faites ces deux analogies 9
I. Corne qnelqH'Hn des citez, C9i»f venant V angle refuisj
A ûuel^m'nne des différences troûvfes j

Ainfi Vautre diffetehce,

A un quatrième nombre^
i. Comme Vautre cet/ cùmf tenant Van^ reigùis^

Au Stnus toial^
^ ,AinJî le^ quatriîfne nombre trofsvf $

À unfeftiémei . . v

Ce feptiéme nombre étant multiplié pir le Sinùi
total, la tacine quarrée du produit fer^ le Sinus de là
mditié de l'angle requis*

Ou plus facilement par togarithmeé ,; ajput^ le
Logaritnme du iinus total au feptiéme Logarithme s
la moitié de la fomme fera le Logarithme du Sin^ç dé
la moitié de l'angle requis. . . ^

Exemple* Au Triangle précèdent foit requis Vtà&^

rkC iiii

Lescptci^AB 8^5

CBC éji

La fomme des cotez 2774 *
La moitié de la fomme 1387

B i/

to C H A P. I II. Des TridH^. feBil. ohli^.

La différence de A B ^ 5 2. i le Log. a. 71 ytf yay

ta différence de B C 7 5 5 le Log. 2. 8 77 9 4^^

la {brome 5* 5 9 5 ^ 1 7 4
te Logarithme de AB . %6^ 2. 9 J 7 o 1 6 1

Le Log: du 4. avec le Lôg. <îu Sin. total 12. ^ 5 8 <î o i j
Le Logarithme de B C 632 2.8oo>i7i

Le tog. du 7. avcd le Log. du Sin. total 19-8578842
La moitié eft le Log. du Sin. de 58 d: (5^ 9. 9 2 8 9 4 2 1
Son double 177 d: 13'. eft l'angle requis ABC.

Ou bien ajoutez les complcmens Arithmétiques
des Logarithmes des cotez c«nprcnans l'angle leqiuis ,
:aax Logatithtnes àes différences trompées , la moitié
de lafommc ftrj^ le Logarithme du Sinus delamoi^
dé de Tangle requis. Comme au même exemple.
Logarithmes.
Les cotez r^ ^ * ^ 5 7-0^20839 compl. Arithm.
- t-B C ^32 7.1 992829 compl. AtiihmT
La diffct. de A B 5 2 2 2. 7 1 7 6 7 o 5
La di|fer. de B G 7 5 5 2, 87794^9 •

La morne de la foimne 9-9289421 comme aup^a-

vant.

V- ' * ' ....

r IV. P Bi^op. Etans conntfs les angles & un côté,
tibuver quelqu'un des autres cotez.

• Comme It Sinus de Vdngle cfffùfé a» cS^é connu ,

Auedté C0nnu,

• Ain^le Sinus de Vangle opfojï aucêtfrequify

Au dté requis.

V. P R OP. Etant connus deux cotez , & l'angle qu'ils
comprennent , treuvetle troifiémc côté.
Trouvez, frcmieremtnt les autres angles far la 2.
Trof. de ce Chapitre , c^ p^s apr/s le côté requis par
la précédente 4. Prop. .

I w

/

i *• i

C A f • I y. Des TriMg. Sfben rcQung. u

y *- x, ' , I I I I I I ■ I I II <! I

CHAPITRE IV.

Dh calcul des Triangles Spheriques reCtangles.

Observations.
f« Q I une des jambes eft Quadrant , l'angle oppofé
i3 â cette jambe fera droit ; fi moindre que le Qusu
dranc » aigu ; Se fi plus grande , obtus : ^ au conttaire.

2. Si une des jambes eft quadrant > l'hypoteRufe fera
auffî quadrant: mais, fl l'une & l'autre (ont moindres
ou plus grandes que le quadrant , l'hypotenufe fen
moindre' que le quadrant : & fi une eft plus grande que
le quadrant * & l'autre moindre , l'hypotenuTe /era
plus grande que le quadrant -, & au contraire.

}. Si un des angles touchans Thypotenufe eft droit »
l'hypotenufe fera quadrant ; mais , fi ^chacun eft moin-
dre ou plus grand qu'un droit > l'hypotenufe fera moin-
dre que le quadrant : & & l'un eft plus grand qu'un
droit y Se l'autre moindre , l'hypotenufe ftrà plus g]ran-
do que le qiiadrant : & au contraire.

4. De tout Triangle jSphcrique lc$ trois angksibnt
plus graads que deux droits^

I« ,P ^ Q p. Etant connu un angle oblique , Su tyy

jambis ^djgçepi:eicet angle, trouver l'^uti^e

aiigte oblique.

Comme le Sinus total ,

^n Sinus de l^ngle pilique connu §
^inj! le Sinus du comfletpient de U jambe connue 9

Au Sinus du complément de V angle requis.

n* Prop* Etant connue une jambe , & un angle
oblique oppofé d cette jambe , trouver l'autre an-
gle oblique : Moyennant qu'on fçache s'il efi aigu
!0U obtus : ou bien fi l'hypotenufe , ou Vautre jambe »
Ci? ^9'^^^^ ou plus grande que le quadrant.

|i € If A 9. Vf. Des Jriangh Spherif. reâ. •
Comme le Sinus du complément de lajamhe connni^

An Sinns 4f^ complément de V angle coi^nn ;
■ jiinji le Sinus total ,

uiu Sinus de V angle requis.

Autrement.

Comme le Sinus total ,

jiU Sécante de la J4mhe connue,
jiinfi le Sinus du complément de l* angle connu 9

Au Sinus de l'angle requis*

1 1 L F n o p. Efranc connue rhypotenufc , & une jat^
be» trouver l'angle oppofé à ccçce jambe.

Comme le Sinus de l'hypotenufi ,

Au Sinus total 3
Ainfi U Sinus de' la janAe connue ^

Au Sinns. de l'angle requis.

Autrement.

Comme le Sinus total,

A la Sécante du complément de Phjfpotâuuji |
Ainfi le Sinus de la jambe connue ,

Au Sinus de l'angle requis*

|V. Prop. Etant connues les janabes , trouver le^»
quel on voudra des angles obliques.

Comme le Sinus total.

Au Sinus de la jambe adjacente k l'angle requis*.
Ainfi la Tangente du complément de l'autre jambe ,

Al la Tangente du complément de l'aygle requis.

y. P RQ p. Etant connue Thypotcnufc & une jambç ,
trouver Tangle qu'elles comprennent.

Comme le Sinus total ,

A l^ Tangente du complément de l'hjfpotenufe y
^infi la Tangente de la jambe connue ,

jiu Sinus dfU complément de i'angle requis*

C H A p. I V. Des Tri4f0gL Sfheriq. reS. ij

VI* P^o p. Etant connue rhypotenufc, & unaiïglc
oblique , trouver l'autre angle oblique.

Comfnt le Sinus totale

A*s Sinus du consplemeut de l'hyfotenufi s
Ainfi la Tangente de l* angle Mique connu ,

A la Tangente du comblement de l'angle re^iSé

V 1 1. P R o P. Etant connue Thypotcnufe , & un angle
oblique, trouver la jambe opppsée à cet ^mglc.

Comme lé Sinus total y

Au Sinus de rhypotenufi -,
Ainfi le Sinus de l* angle oblfi/ue connu ,

A^ Sinus de la jambe requife.

VIIL Prop. Etant connue Thypotcnufe » & une
jambe , trouver Tautie |ambe«

Comme le Sinus du complément de la jambe connue 9
Au Sinus du complément de l*hypoteuufe ,

A^^fi le Sinus total ,

At^ Sinus du complément de la jambe requife.

' AVLtKEHnVJ.

Comme le Sinus total ,

A la Sécante de la jambe connue : ,

'Ainjî Le Sinus du complément de Vhypotenufe ,
Au Sinus du complément de la jambe requife.

IX. P R o p. Etans connus les angles , trouver laquelle
on voudra des jambes.

Comme le Sinus de V angle oblique adjacent k la
^ jambe requife ,
Au Sinus du complément de Vautre angle obliques
Ainfi le Sinus total ,
A» Sinus du complément de la jambe requife.
Autrement.
Comme le SinUs total»

A la Secaiite du complément de V angle oblique
adjacent à la jambe requife ,

B iiij

%^ C H À p. f V. Des TriângL Spherif. re&.
^infile Sinms du complem. de VâHtre dngle okli^Ui f
Ah Sinjadu cemplepunt de léf jambe retjuifié,

X. P R o p. Etant connue une jambe » 9c unang|e

oblique adjacent à cette jambe ^ trQUVçc
( i'atttre janipef

Coff^me le Sinus tetal ,

Au Sinus de la jambe cennuêy
Aiujî la Tangente de l'angle ebli^ue cenuu «
^ la Tangente de la jambe requife.

Kl. P R o p. Etant connue une jambe , ic un angle obli^
que oppofé i cette jambe , trouver l'autre jambe s
Moyennant qu'enfçachefi eUe y ou bien l'hyporenu*

' S^y efi moindre OU plus grande que le quadxa^tiom
fi l'autre angle obliquf efiaig^AU ^btus. -

Cpmme le Sinus totale

A la Tangente du complément de V angle oblifUê
connus
Ainfi la Tangente de la jambe conpi^e^

Au Sinus de la jambe requifi.

JCII. P R o p. Etaqt connue Thypotenufe , & pn angle
oblique, trQUver (a jambe adjacente ^ cet angle.

Comme le Sinus tot^l j.
Au Sinffs du con^plemfnt de V angle fbli^ue c^nnpp

Ainfi la Tangente de (*hypotenufe ,
A la X^ngente de la jambe requifi.

XIII. P R o p. Etans connus les angles ^^
trouver l'hypotcuufc.

Çpmme le Sinus totale

A la Tangente du complément de l'un des a»^
gles obliques i
^.inftlaTangente du compL de Vautre angle obliqu^

^u Sinus du complément de fhyjftenuji.

p

I

Chj^p.IV. Des TriângU Sfheriq. reÙ. îj

K i V. P K Q Pf Etans connues les jambes » Cf pnyer
Vhypotenufcf

Comme le Sinus total f

Ah Sinus du comblement iune JesjéUÊ$tes /
jlinji le Sinus du complément de l'OtUtre jambe »

Au Sinus du complément de Vhjfotenuje.

XV. P n o p. Ectiit connue une janabe s & un angle
oblique oppofc à.çecre jambe , trouver l'hypocc-
nufe : Moyennant qu'on /fâche Ji elle , ou Vautra
jambe , efi moindre ou plus grand que le quadrant «
ifu fi l'autre angle oblique èfi aigu qu obtus.

Comme le Sinus de l'angle oblique connu ^

Au Sinus de la jambe connue ^
Ainfi le Siffus total ,

Au Sinus de Vhjpotenufi»

AutR|!MENt«

Comme le Sinus totale

A la Sécante du compU de l'angle oblique connu i
Ainfi le Sinus de la jambe connue ,

Au Sinus de l'hypotenufe.

X V I. P R o p. Etant connue ime: jambe , & un angle
oblique adjacent à cette jambe > trouver Thypotenufe^i

Comme le Sinus total <,

Au Sinus du compl. de V angle oblique connu :
^infi la Tangente du compl. de la jambe connue ;

A la Tangente du compl. de l'hypotenufi.

CHAPITRE V.
Du calcul des Triangles Spheriques obliquangUs.

POur résoudre la plufpan des Triangles Spheriques
obliquangies , on les réduit en deux Triangles re- .
^angles , par une perpendiculaire y pree du bout do

^ C R A p» Vi Des TrldHgl. Spheri^. ûhliij.
cote connu ayant à Tàutte bout un angle connu > (ûr
la bàfe , prolongée s'il eft neceffaire. Et alois 09
trouve les termes requis par les termes connus des
Triangles reâangles. Or puifque la manière par l'in«
vemion de la perpendiculaite,qui demande trois ope-
rations au moins , eft déjà vulgaire , & peut être faite
par les Propoiîtions precedentesije n'en diray nK>t,pouc
montrer comment on réfoudf a les Triangles fans l'in^
ventiôn de la perpendiculaire par le moyen de deux
Propo(iti6ns feulement ; Et au lieu de pluificurs paro^
les qa il faut pour les exprimer , je le feray plus brie-
vement par lettres. Ceux qui défirent en avoir les^dc-^
monflxations , les trouveront en \zTrU0n0nutrie Sri^
tanni^ue d* Henry Briggs*

Pour ce faire fclon les Analogies fuivantes , mar*
quez le Triangle propofépar les lettres A ^BjC, fça-
voir langle duquel la perpendiculaire doit tomber par
la lettre A , Tangle connu adjacent à un cocé connu
par la Ictrre B , & le troifiéme angle par la lettre C ;
fie où la petpendiculaite coupe la bafe à angles droits >
mettez la lettre D. Les angles étant ainlî marquez,
les cotez de chaque Triangle reâ:angle feront auffl
marquez.

Si les angles B & C , touchans la bafe B C , font
aigus , la perpendiculaire tombera dans le Triangle ;
il B eft obtus , elle tombera dehors ap dcU rangle^oh*
tus C.

Remar^He.

Ptiis qu'il eft dit que la perpendiculaire doit tomber
du bout d'un côté connu ayant un angle connu à l'au-
tre bout , & que cela en quelque cas , comme de la
|. 4. «9. & 11. Pfop, peut être fait en deux manières :
partant en la 4. & 11. Prop, nous avertiront doù I^
perpendiculaire neceflairemcnt en cette rencontre doit
tomber. Aux autrc$ deux il n'y a point de diiference.

I. P R o p. Etant connus deux angles , 8c le c&tê
d'cna'cux , trouver le troifiémc angle.

» » eu

1

I. Comfke le Sinus tetat >

Ah Sinus dû ccmfUment de A B

V^/>r/?. Al Tangente, de ABC

A la Tangente - du comblement de B A D
Etant trouvé BAD Ton connoîtauffi CAD.

%. Cçmme le Sinus de BAD

Au Sinus de CAD

^inj! le Sinus du cemflement de ABC

Au Sinus du complément dç A C D

Remarque.
En la première & féconde figure , A C D eft le me-
nie que A C B : mais en la troifiéirte , ayant trouvé
A C D , il faut prendre (on complément à 180 degrez >
polir avoir l'angle requis A C B.

Pour montrer la facilité de calculer par ces analo-
gies 9 je donneray un exemple , ^vec la plus bricvc
manière d opérer.

Soit du premier Triangle obliquangle BAC , connu
l'angle B A C 104 deg. 6. l'angle A B C 38 deg. 6. & le
irôtc A B 30 deg. 6. on demande l'angle A C B.
I Logarith. 2

Logarith.
Si.co. p.8^5}ix
Sin. 0.0818525 à.c.
Sin. <,.87i(>4r4

Si.CQ.ifj.Sjoôiijç

AB jo d. 6. Sin. comp. 9.937530<S
ABC 38 d ô. Taftgente 9.89x8098

pAt5 55 d. 55'Tan.com.i9.8j03404

CAD 48 d. 5' •. . •

AB 44 d. 5e • • f , • • « «

j»l C R A r • V. Der Triânfr. Sfheriq* Mifii

IL P K o 9. Etans connus 4eu]( cotez , te i'anglc^ oppofé
i l'un des deux > crouret l'angle qu'ils comprennent.

ç*-ix

I. Cpmme te Sinns utal , . , ^

A» Sinus du cùmfUment de A B

Ai^nfi U Tangente de ABC

A U Tangente dm cçmflementd^ B AD

a. Comme U Tangente de A C

A la Tangente de . AB

Ainji le Sinns an complément de B A D

. An Sinns dn complément de CAD

Si la perpendiculaire tombe dans le Triangle, la fom«
me de B A D , C A D ; fi dehors , leur difTereiiice eft
l'angle BAC, qu on cherche,

IIL P R o p. Etans connus deux angles , & le coté op-t:
posé à Tun des deux trouver le troifiéme angle i
Moyennant tjn* on fçache s'il efiaign on obtus : on
hien <}ue Veffece du cètéoffoféà l'autre anj4e donnf
foit connue^

I. Comme le Sinus f ot al ^

\4^ S^nns du çotnplçn^ptd^e

AB

CUÂT. V. Des Triânit.Sfheriq.bhliql ï|

sAinJi la Tangente de ABC

A ta Tangente du complément de B AD

1. Comme le Sinus dn complément de ABC

jin Sinus du complément de B C A

Ainfi le Sinus de B A D

Au Sinus de CAD

Si la perpendiculaire tombe dans te Triangle > la
fommc dcBAD,CAD:fi dehors , leur différence
cft l'aiîgic requis BAC.

IV. P R o p. Etant connus deux cotez , & Tangue qa*ik
comprennent i trouver quelqu'un des autres atij^es. .

En ce cas la perpendiculaire doit necelTaireoienc
tombei: du côté oppofé à l'angle qu'on cherche*

I)

I. Comme le Sinus totale

Au Sinus du complément de ABC

Ainfi la Tangente de A B

A la Tangente de BD

Etant trouvé B D^ fe maaifcfte auffi C D«

X. Comme le Sinus de CD

Au Sinus de BD

Atnji la Tangente de ABC

A la Tangente de A C D

KemurejUe.

. En U première & féconde figure , 1 angle A C D eft

le même que A C B : mais en la troifiéme ayant trotf-

vé A C D , il faut prendte fon complément à iSo de*

^tez , pour avoir Tanglc «quis ACB.

y.*J?JLop. Clans copnusdcuxeôtcz, &rangleopp(>*
fi à l'un des deux , trouver l'angle oppofé a l'autre i
y^ AiByennanijju'onfçAçhe s'il ^fi digm 9h obtMSi-

l': Çmm€ le SinHs du cote offoff à l'angle connu,
\, Ah Sinus de t angle connu ;
jiinjîle Sinus de Vautre côté connu,
'Au Sinui de f'anglt requis*

VL Prop. Etans connus Jjcç t|pi$<:ôtje9 » trouver
lecjuel oti voudra àz% angles.

^5oÔtez ejifcmbie les trois çôtçz , & de U îDoitic dé
îciir fomme (buftray CE chaque côte comprenant Tan-
glë requis > bdul: >voir leurs dtfer€nces< Apte^ celai
^fuivc» ces deux anj^lo^jes.

jf^Comme le S^s^us de quelqu'un ^s citez* com^re-^

17'^^^. ff^^s l*T0tgle reqffis y • *

\ \ Ad.Sinus deVpihè des differeffées troUi^ùs :

iÂhtJi le Smus dé /autre diffirknc<f,

\ \ A ftn^qHatriétne^ Sinus. ' .

.^vCofjfmé le Sinus de Vautré cêté^eomprgnant Van j^
gle requis, ,

Au Sinus fotaly' ; ' /

* Ahjfile quatrifmé'SinUs tréuvé\. . .\ . ^

A un fepiénie Sinus* , .

Ce Çcptiéme Sîpus étant muïtipUc par le Sinus to-
tal, ktacine quarrée du produit fera le Sinus delà
tticÂic de l'angle requis. ... > v .

Ou plus facilement par Logatithmesl , ijoûtez le
Logànthmc du Sinus total au fcptiémc Sinus Loga-
ritlwnâque-.la moitié de la fommcf<ira le Logarithsic du
Sinus de la moitié dei angle requis.

Ou bien àjoûtezrles compicmens Arithmétiques de»
io^arithmcs dés Sinus des cotez comprenant l'angle
requis , aux Logarithmes èit% Sinus des différences
tfouv'ëes : la moitié de ia {bmqae fera le Logarithme

f

CtiAP. V. Dts TriâHg. Sfhtriq. oUiq. H

Ha Sinus de la moitié de l'an-
gle requis» donc voicy un exezn«
pie.

Au Triangle A CD font
connus les côcez B D 41 d; 8^
AÇ30 d: ô. & CD24d:4.
On demande Tanglc A C D. '

41.8'
30.0
14.4

AD
AC
CD

La (bmme des cotez

iLamoitié

ta ditfer.deAC

La ditfcr. de C D

La foniDic

La moitié eft de

Le double eft

ii.6
14.x

51.58

Comf1, jirithf».
o.30io50{i

0.3895SJ5

Logarithmes*
5^-49i}o8|
9. (^ o 9 8 8 o 3

de ACÎ>

VILProp. Etans connus les trois angles 9 tfomct
lequel on voudra des côitez« '

En changeant les angles en leurs cfttc^ oppofeï 9 6t
prenant tu lieu du plus grand angle 6c du c6té oppofé
a cet angle > le compleinént à 180 degrez , l'opération
fera tout de mSme comme en la précédente.

V 1 1 J. P R o p. Etans connus deux angles , & un côté
oppofé à l'un des deux trouver le ci^té oppofë i
l'autre : Moyennant ejH'^tn ffocbe s' il e^ moindre oh
flui grand fue le quadrant.

Comme le Sinns de l'angle oppos/an cSt/connu g

Ah Sinus du mime côté:
Ainfi le Sinus de l'autre angU connu ,

Au Sinus du c6t/ requis*

I X. P & o p« Etans connus deux cotez » & ràngfe
(qu'ils coinptennenc» trouvetlé cioifiémc c&céf.

%• Comine le ^jnHS total > :

^u Sinus du complément dé A B C

Ainfi U Tangente dé A B

AU Tangente de BD

^ Etant trouvé B D , l'on conhoic auffi C D.

f. Comme le Sinus dû complément de É D

Au Sinus du complément de C D

: A^^ l^ Sinus du complément de . A B

Au Sinus d» complément de AC

%. P Ji'o p. Etans connus deux angles » & le coté pp.
pofé à 1 un dies deux , tfouver le cotdcmie les angles

; connus : Moyennant ^u'on ffache file cSt/^ requis ,
ou bfen le cet/ oppojé à Vautre angle connu , r/F
moindre ou plus grand que le quà£ranti

\. Comme te Sinut total »
Au Sinus du complément do

Ainfi la Tangente de
A la Tangente de

Ç J>

ABC
AB
BD

i. Comme

CitAP.V, Des Triàng. Spbtriq. ^Uin. ^^

if^Comme la Tangente de A C B

^la Tangente de , ^ ABC

Ainji le Sinus de . BD

Ah Sfnus de CD

Si la perpendiculaire tombe dânl le Triangle 5 la
fqnifflc de B D yC D : (î dehors > lOir différence ifk
ie côté requis BC. '"

XI. PnoP.Etansconnus deux cotci ,& l'angle ôp-
pofé i l'un des deux , trouver le troifieme côté.

1. Cmme ie Sinus total ,

' Au^ Sinus du complément de ABC

Amp la Tangente de AB

A la Tangente dfi BD

1. Comme le Sinus d»tomfte$Hent dt A B

Au Sinus du complément de A C

Ainfiie Sinus du complément de J- R

AtÊ Sinus du complément de CD

Si la perpendiculaire tombe dans le Triangle, la

fûrômc de B D , C D t fi dehors $ Itur différence cft

le côte requis B C*

XII. P Ro p. Etans Connut deux ahgks , & le côté

d'entrc-deux , trouver Icqueh on voudra

des autres cotez.

Remarqué •
En ce cas la perpendiculaire doit neceflaîremcfll
tomber de Tangle connu adjacent au côté reculs.

34 C H A p. V. Dei.TrUHgl. Sfheriq. eiiiq.

^<^B

I. Comme te Sinus total ,

Ah Sinus du complément de ^ A B

Ainji là Tangente de ABC

A U Tangente du complément de B A D

Etant trouve B A D , fc xnartifeftc aufli CAD.

i. ComtHè le Sinus du complément de CAD

Ah Sinus du complément de B A D

Aif^fi la Tangente de A B

Ala T^angente de .• .AC

Abrégé de ^u^ions Aftronomi^uây. '

t; TJ Tant connue la plus grâhdfc obliquité de ITkfi-
JEptiquc, & ladiftancc 4i ScJcil »i-plus proche
Ec^inoxe , tretavtt fa dcdin^ifon.

tomme le Sinus tdtàt j
, \^^ Sinus de la dijhndè m pt^s ftèche £dfU4W^xei
Ainjî le Sinus de Id plus g^lMk èfhii^Ui^,
Au Sinus delà déclinai fin reéjUife.

îï. Etant cohnùc la plus grabd* okliquité de l'Edi-
ptiquc , & la déclinai fon du Soleil,. iïouv« le lied
. du Soleil dans TEcliptiquc..

Comme le Sinus de la plus grande obliquité de l'Ècli^
ftitjue , . .
Au Sinus de la declinaifin du Soleil ;
AinJi h Sinus total ,

Af^ Sinus de la diJlAncé dn Soleil au plus proche
Bqninoxe^ ^ '

iprc-
:confc-
<juenc il faut opérer poui Us dcclinaifons cxaétes.

III. Etant connue la plus grande obliquité de rEcii-
prique. Se la diftance du Soleil au plus proche Equi*
noxe> trouver fon Afcenfion droite.

Comme le Sinus tôt 41»

Ah Sinui du complément dé ta fins grande ^bliqnitty
Jlmfi bk Tangente de la défiance dn Soleil auflnsfro-
eheEqninoxe ,

A la Tangente ^de4' Jlfctnfion droite requife.

I V. Etant connue la plus grande obliquité de TEcli^
:-ptique , & iàdtctinairon du Soleil » trouver

i . fbti Afcenfion droite* v
Comme le Sinus total i
: AlaTangente deladecUnaifon du Soleil i
. tMfrifi M Tangente dss complément de la f lus grande
otliquité^
Au Sinus de Vjijcfnjion droite reqnife. '

y. Etant connue Isplus ^ande obliquité de PEcIipti-
quç;, &JadiftancedttSolcAai^ pUis /proche Equi-
noxe , trQuyer l'angle que rEçlipnque fait ^ avec ]fi
Méridien;
Commi^le Si^ûs total i \

Au Sinus dù-éhmflément de Ik difiance du Soleil
au plus proche Eqsiinoxe^
Ainfi. la Tangestitdje la plus grande obliquité ,
A la Tavgemê du complément de fan^e requis.
VL Etant connue la plus grande obliquité de l'Eclipti-^
que> Se la decliuairon du Soleil , trouver latigle
que rÉcliptîque fait avec le Méridien.
Comme lé Sinus du complenfent de la dficlinaifçn dsf
. Soleil,, , ,;

Au Sfnus dficompL de la plus grande oUiquipé}
Ainjî le Sinus total

Au Sinus de Vângle requis.
■ C ij *

3C Ahngédis J^ejlions AJlrcnomitjiêe^s.

Vit* Etant connue la declinaifon du'Soleil y & Tél^
vation du Pôle i trouver l'ampUcude Orientale o\x
Occidentale du Soleil.

Comme le Sinus ducemplem. de V élévation in Pçte ,
Au Sinus de la declinaifon du Soleil j

jîinfi le Sinus total , ^

Au Sinus de V Amplitude re^uife.,

yill. Etant connue la diftancé dtt Soleil ^au pluspro-"
che Equinoxe , & fa plus, grande. ArapUtude ,
tR»uver les autres. Af&pUcttdes. \ ^ ' ..

<lomme le Sinus totale '• ' " ^.r:- .V r

Au Sinus de la f lus grande Amplitude d^'SdMls

Ainfi le Sinus de Jà dipakce au-f lus proche Equinoxe
Au Sinus de l'amplitude refuifié. ( .\ ^v:...'V3

IX. Étant connue la dcclinaîfoû dû Sblçîl ;, Jfe Icle-
* vation du Pote , trouvet la' diffctclnce Afcjciifîonèlle.

Comme le Sifius total ^, ; r ' . ^ j.»

. . A la , Tangente de la decîjnaifqn du Soletl i
' : Ainji. là iTangenti^e VÏl^ydiidn du Pifé ; '' ' • ''
Au Sinus de la ^i'grrèncc AJcenJionek^^^

X. Etant connue fa declinaifon 'du 5^oleiL,'&Vâcva-

tion du Pôle , trouver rhcurc.du^ Icycr pm,*>
• du' coucher, ilu^^oïcil*

Comme le Sinus total 'y:-'.

A là Tangente de Ik decUnaifondû S^lèU :
Ainfi la; Tangente de Vélevation du Pote y ^
•Au Sinus du complément de VatcfeminoÛHrne.
L*Arc femînoifttirne réduit en tiçmps , donnera l'heu-
re du lever du Soleil , cjui ctant otc de ii, heures , il
reftera l'heure du Coucher. '

XL Etant connue rEleyatipn du Pôle ,& l'heure du
lever ou coucher du Soleil , trouver fa declinaifon ,
& partant à quel jour il fe lève & couche a rfaeu-
xc donnée.

Abrégé iè ^jie fiions Afironomiques. ^ jy
Comme le Sinus total,

Afè Sinus de U difiance du Soleil du Midj /
A'tnfi la Tangente du compL de V élévation du Pôle ,

A la Tmgente de la Declinaifon requife.

Maintcnaqt pour avoir le jour auquel le Soleil fç
levé & fc couche à l'heure donnée , faites cette ana-^,
logîc.

Comme le Sinus de la f lus grande obliquité de rE^
cliptique y
Au Sinus de la déclinai fin du Soleil ;
Ainfi le Sinus total , •

Au Sinus de^ la difiance du SoUH au plus pro^.
che Equinoxe.

XII. Etant connue Télcvation du Pofe , la déclinai (on
du Soleil , ic Theure du jout » trouver la hauteur y
du Soleil.

Cette Méthode fuppofe la perpendiculaire tirce^d»'
Pôle de l'Hotizon fur le cercle Horaire du Soleil.
i. Comme le Sinus total ,

A la Tangente du complément de Vélevation
du Pôle ;
Ainfi le Sinus du complément de la difiance du So-
leil du Midy ,
A la Tangente du premier arc trouvé.

Depuis fix heures du matin jufques à fix heures
du foir, ôtezie premier arc trouve deladiftançe du
Soleil du Pôle , mais il le faut ajouter depuis les fix
heures du (bit jufques à fix heures du matin , pour
ayoir le fécond arc trouvé.

I. Comme le Sinus du compl. du premier arc trouvé^
Au Sinus du complément du ficond arc trouvé y
Ainfi U Sinus de l'élévation du Pelé ,

Au Sinus de la la^ hauteur requifi.
Pour trouver la hautepr du Soleil à fix heures,,
CxAvcz cette analogie.

C iij

5^ Àiregf de ^^efiions jffiron^miqueu
Comme h Sinus total,

j4u Sinus de la declina'tfon du Soleil : -
Ainji le Sinus de V élévation du Vole ,

Au- Sinus de la hauteur reefuife.
l^our avoir la hauteur da Soleil au temps des Eqoî-
noxes , dites >

Comme le Sinus total. ,

Au Sinus dû complément de V élévation du f oie i
Ainjile Sinus du complément de la difiance du Soleil
au Midj ,
Au Sinus de la hauteur, requife.

XIII. Etant connu TAzicnuth & U dedinaifbn da

Soleil ) avec Theuce du jour , trouver
la hauteur du Soleil.

Comme U Sinus de l'Az,imuth du Soleil du Méridien»
An Sinus du complément de fa declinaifon ;

Ainfi le Sinui de fa diftance au Midy ,

Au Sinus du complément de la hauteur reifSiifi.

XIV. Etant connue* la déclinaison, la hauteur ».&
TAzimuth du Soleil, trouver l'heure du jour.

Comme le Sinus du complément de la declinaifan >
Au Sinus du complément de la hauteur ,

Ainjtle Sinus deVAz.imuth du Méridien ,
Au Sinus de la difiance du Méridien.

Cette queftion cft fort mile pour trouver l'heure
plus facilement que par la fuivante, pourvu qu'on,
^t une ligne Méridienne Horizontale bi«î tracée , ou
un bon Aimant : parce qu*obfervant avec 1 ombre d'un
iîlet Tangle de l'Azimuth en même temps que la hau-
teur, vous aurez l'heure par une feule analogie.

XV. Etant connue Télevation du Pôle , la declinaifon ,
& la hauteur, du SoleiU trouver rhcure du jour.

Ajoutez enfemble ces trois chofes : Le complément
de Tclevâtion du Pôle \ la ^î^%tkcc du Soleil du Polc y
& le complément de la hauteur du Soleil : & de la

moitié de leur (bmmc fouftraycz^ le' complément de
Télevation du Polc^ ScU diftance du Soleil au Polc^
afin d'avoir leurs différences. Après cela faites ces
deux analogies :

1. Comme le Sinns du comflement dé l'élévation dn

Pôle,
Âh Sinus de Vune des différences trouvées ;
Ainfi le Sinus de Vautre différence ,
ji un quatrième Sinus*

2. Comme le Sinus de la difiance du Soleil au Foie y

Au Sinus total y
jiinfi le quatrième Sinus trouvé ^
A un feftiéme Sinus.

Ajoutez le Logarithnoe du Sinus total , au feptiénie
Sinus Logarithniique : la moitié de la fomme fera le
Logarithme du Siaus d'an arc , lequel étant doublé û
teduit en heures , donnera la ^ift^ce du Midy..

Ou bien ajoutez enfemble les complemens Arithi>
metiques des Logarithmes du Sinus du complément
de l'élévation, & du Sinus de la diftance du Soleil au
Pôle , &^ les Logarithmes des Sinus des différences
trouvées : la moitié de la fommc fera le Logarithme
du Sinus d'un arc , dont le double étant réduit en heu^
res donnera la diftance du Midy.

Cette queftiori tombe des plus en pratique , & fe
refout par la(». Prop. du Chap. V. des Obhquanglcs»
Car au Triangle ABC, les trois cotez font donnez.
C, eft lePole.
B,rAftrc.
A C , complément de

la Latitude C K.
A B , complément de

la hauteur BH.
BÇ, diftance de l'A-
ftre au Pôle » qu'on
i^ait en otant fa decUnâifon de 90. degrez , quand

C ui)

4<> Alregi àe ^ueJUons Àflrônomiqies.
€llc cft Septentrionale , & l'ajoutant i ^o. Aigtt%^
lors qu elle cft Méridionale , &: qu^ la Latitude cft Se-
ptentrionale : car fi elle étoit Méridionale, il faudroit
opérer tout au contraire.

Le requis, cft l'angle A C B > ou la diftancc de l'A-
ftrc B au Méridien 1 A mefuréc par l'arc de l'Equa-
tQUr IL) qu'il faut réduire en heares , en le divifanr

par 15-

Or cette Qaeftion fc refout plus facilement par Jjc

4cf nier précepte » ç'eft à dire par les complemens
Arithmétiques , que par les autres opérations.
£tant cofinné l Elévation du^ Pôle , la hauteur ^ çj- la
Declinaifon d'une Etoile , trouver l'heure
de la. nuit.
' . Il faut faire comme pour le Soleil , & on aura l'an-
gle A C B , ou la diftancc de l'Etoile au Méridien ,
îaqucllc il faut ôter de fon Afccnfion droite , fi Tob-
fcrvation cft faite dans la quarte d'Orient , ou l'ajoù-*
ter, n elle eft dans la quarte d*Occident : & on aura
TAfcenfion droite du milieu du Ciel , de laquelle
enfin fi on ôte TAfcenfion droite du Soleil , il reftera
la diftancc dq Soleil au Midy paflc , laquelle étant
rcdqite eh temps donnera l'heure requifc. Mais , fi
l'Afcenfion droite du Soleil fe trouvé plus grande que
celle du milieu du Ciel , il faut ajouter à cellc-cy
jtfq. dcgrez, pour en pouvoir fouftraire celle-là, afin
d'avoir la diftancc requife du Soleil du Midy pafle , qui
eft l'heure que l'on cherche , étant réduite en temps d
15. dcgrez pour heure.

Étant conf^ le lieu du Soleil , ^ V Elévation du "Bole ,

trouver l'heure du commencement & de la fin

^ des Créfufiules.

Dautant qu'on détermine ordinairement la durca

des Crepufcules par le temps qac le Soleil cft abaillc

fous l'Horiaon , j^ifqucs à 18. dcgrez , étant certain

qu'il employé le même temps à defcendrc de 18* de,

grez de hauteur jufquosçnl'HQriaBonque de THori^

zon jafques a 18. degtez ou deâbusr, qui tftléCre*
pufcule du foir 9 & é^ tn&me â monter le tnatiti.

De façon qu'ayant l'heure de la hauteur , &fçachànt
celle du lever ou du coucher par la Queftion lo. leur
dijffcrcnce fera la longueur du Crepufcule , laquelle
étant ôtée de Th^ure du lever du Soleil , vous autes
le commencement duîour,& étant ajoutée à l'heure
du coucher du Soleil » vous aurez U fin du jour.

XVI. Etant connue l'Elévation du Pôle , laDedinai-
fon & la hauteur du Soleil, trouver fon Azimuth.

Ajoutez enfemble ces trois chofes : le complément
de l'Elévation du Pôle , la diftance du Soleil au Po«
le » & le complément de la hauteur du Soleil , & do
la moitié de leur fbmme (buftrayez Le.complement de
l'Elévation du Pôle y & le complen^ent de la hauteur
du Soleil , afin d avoir leurs difFcrenceSt Après cela
faites ces trois analogies.

I* Comme le Sinus du comblement de l* Elévation
du foie ,

Au Sinus de l'une des différences trouvées |
Ainji le Sinus de l* autre différence ,

A un quatrième Sinus'

X' Comme le Sinus du complément de la hauteur du
Soleil ,

Au Sinus total ,
Ainfi le quatrième Sinus trouvé ,

A unfeftteme SinUs.

Ajoutez le Logarithme du Sinus, tolalaufeptiéme
Sinus Logarithmique : la moitié de la fomme fera le
Logiarirhme du Sinus de la moitié de l'Azimuth re-
quis du Septentrion.

Ou bien ajoutez enfemble les complemcns Arith-
métiques des Logarithmes du Sinus du complément
de l'Elévation du Pôle , & du Sinus du complément
4w la hauteur du Soleil > icUs Logarithmes des Sinus

4t JÈiriffie ^fffftimi '^AJhûnmi^Ufr.
éai 'Stkfcnots trouvées : la nsoicié 4e 1^ Commit Çct^
le Logarithme du Sinus de la moitié (ierÂziinmhie-«
quis du Septentcioa*

Cette qoeftion fe cefbut comme la précédente pac
la 6. Prop. des Obliquangles > les tcois cotez du Triafi-»
gle AB C étans donnez eti la figure de cy-devant :
car ayant trouvé Tangle C A B » fon complément BAI ,
ou H AM fera l'Azimuth requis du Mtdy i l'Aftre.

. Elleeft fort utile pour la (7)^awoif/^jy^ & la varia^^
iioH, ic VAjmAnt , car en pbrervant la hauteur du
Soleil on peut marquer fur un plan Horizontal l'om*
bre dun filet perpendiôtlaireî pms> VandeAzimu*
thaï étant trouvé par le calcul > & tracé iur le piM ,
on â bu la ligne Meridèene , ou la lipté OriintaU y fé-
lon qu'on a pris le compkment de l'angle CA B fut
iSo ou 90 degrez » par Tune ou l'autre defquelles on
trouve la variation de l'Aimant.

Pour faire les Tables d'Azimuth» (èrvans àla Gno^
monique &c aux Qgadrans de l'aiguille aimamée > i!
fuific d'y mettre les commencemcns des Signes. D»
Henrion en a fait pour plufîeur$ Elévations dans (on
Traité des Triangles Spncriques.

Pour trouver 1 Azimuth du Soleil à 6. heures , fut-
vez cette analogie.

Comme le Sinns total,

Af* Sinus du complément de VlElevatlon du Pôle,
A infila Tangente de la Déclin ai/on du Soleil,

A la Tangente de l'Ax,imuth du Soleil vers le

^ . Septentrion.

Pour trouver l'Azimuth du Soleil au tctops des
Equinoxes , faites cette analogie.

Comme le Sinus total ,

A la Tangente de l* Êleifatio» du Soleil i
A n fi laTangente de V Elévation du Pôle ,

Au Sinus du Cûmflement de VAx^imuth reculs
du Méridien^

'jttregi Je J^ftiàns jtfim'nûmiqnetp . 'jff

X ^ H. Deux hauteurs de Soleil od4ie quelque Aftre »'
dont la Dedinaifon foit connue, étansobiîbtvéer
en un joucouen uneiittit> aveiclairdi&feocrAjsW
mutalestrouver TEIeirationdtt Pole»& leur Azimuth^

AB.CD eftlçMeridien,

C Zenith. D Polc.

BEprEquateut.

AIL l'Horizon.

G,& H , le Soleil) ou
TEtoile.

G£,&HKl€ur Dedi^
iKiifbn.

G I , & H F leur hasiteur.

IF dtfference Azimatale.
On demande TElcTa-

tion du Polc D L , & Tare de l'Horizon L F « ou A I ^^

ou AP.

Pmfqu au TriangleC CH , les deux cotez G C , &

H C , complcmens de G I , & H F , & l'angle G C H ^

qui eft IVrc IF, font connus t TarcGH, & Tangle

GHC feront auiS connus.
Mais, au Triangle GDH,lesc&tezGD,&HD,

eottplemens de la I>eciinaifen GE , HK, & GH

ctans connus , l'angle G H D fera auffi connu > duquel

fi on 6tc G H C , reft^ra l'angle C HD : &: partant

dans le Triangle C H D , les deux cotez C H , &

D H , & Taille qu'ils comprennent , étans connus »
le côté C D fera auffi connu » dont le complément
D L eft VElevathn du Pôle. Comme auffi l'angle
D C H , qui eft l'arc derHorizon F L , dont le com-
plément A F eft Tangle de la ligne Meridiene & de
TAzimuth de rAftreobfcrvccnH. Mais fionnepre-
noit que F L , pour complément de 90 degrez , ou
auroit l'Azimuth de la ligne Orientale Septentrional,
fi ledit arc F L étoit moindre que 50 degrez , ou Mé-
ridional 9 s'il écoic plus grand.

4^ 'Mnglde ^^hnî AftroHèmiqueî. ^
"^ Cette Queftion fe peut aiftmeiit réfoudre avec le
compas (iir un Globe» oillles Âzimmhs ti\t$ Almu-
cancantts (bnc tracez , en mettant la pointe du compas »
ouvert des degr^z 'H D » fur les points H , G , & en
£dfanc dèusc inter feâions de cercles au point D , qui
fera le Pôle , duquel on verra la hauteur 17 L , & Tare

L'utilîté eft gràhd^our Ixvéiriatian de t* Aimant ,
parce qu'en ob^ctvant l'angle de quelqu'un de$ h^i^
mâtbs avec rkigiiiUlé , bn^rçait cejby! qu'elle fait avec
I^ Méridien , quand^Ue eft par après trouvée , ce
cji'oîî litf pcut^fakc que par les Afûplitudcs , ou par la
Ii§ne l^endiene , que Ton n'a point fur Mer.

Elle fertauffi pour \k C7if^9iM»/^^ aux plans Hori-
zontaux f mais infiniment plus en ^tous plans qfiicU
qu'ils foîentren ofcfervant deux p
points d'ombre B , C , de U
pointe d'un ftyle D , de l'inciden-
ce de laquelle A, drant deuxli*
gnçs A B y h Ç '9 on aura Tanglc
ou différence Azimûrhale BAC »
la longueur de chaque ombre ^i ^^

A B i AC , & la h^tcut du ftyle , ^

AD, donner^ la hauteur du Soleil fur le plan lors da
chaque obfervation.

Partant on eft dans les termes dçla queftion, pat
lefqueh on trouvera l'art- ,
gle de la ligne Meridtene
du plan , qu'on appelle //-
gnc du Style ,. avec quel-
qu'un des Azimuths AB,
ou A C , laquelle ligne
Mcridicnc ayant tr^cç fui-
yant cet angle, 8c. fur cette ligne FAE ayant élève
le ftyle pcrpcndiculaitc A D , on fera l'angle A D E
complément de la hauteur du I?ole furie plan , laqucU
le ou trouvera comme il a ctc ôafcignc cy devant. Le

point £ fera le Véritable Pôle ott centre du C^a^an
de ce plan ^ duquel' abâiflànt ou traçât la: vericliblc
ligne Metidienriey ^ tinCnt le rayon Equinoxi^ Dï'»
on fera dans lei$' tel?À>es dé parachever ficilcmetit fe
Qàadratic, &de%Vok, ïî'onvcut, PélcTatiôtt db
Pote an lieu 9 lâDediMtfon du plan, &6 llktify^
fe faut fervir du jiTgeméif t en la détermîiiatioti de HVit*
^linailbn, Inclinaifonj &;.autFë9^<:ireoilftancés-s'il7en
^ ,'ruivanr. les Règles de la Qnomonique qu'il fefok
jtôp long de dedviKÇ içy par, le menji* -

}^VIJL Etant coi^niië rélevationdu Pôle , Jk I^di^an»
ti^^' Soïçiï ah Mcn4iciii ^ qui cft rhcure , trbuycf
ï^tc de l*Hori2;oîi éofnpriî entre .ce ^ïeri^icn & ]c

♦ ccfêie' rîof àirc' ' ■'' ■ \ : . . ' \ -^ ' ', ^ • ; ■ '■ :'; :'■ :" '/

Çpmmfi le SinH$ t^tal »' -• ' .-r...*: jr:? ..::. • .j ûi

j< /4 Tangente de l'arc requis. of.n

, Par Ji- oarfçra^facilemçnr^.^y,«q.jçflw(ïe .un Qgjt
dcanc Horizontal , parce: quç iï^i.fiiicçf i^ç llHif^ifûn
jfont ïcRÛI)lç9\cntég^U3ç aux ftû^efei^S.Ji^UlISf éti-
res avec la Meiidiene. -r r ri;\'i'f> fîf •\^..I-7
XIX/Ekant connue ktx>o'gttude^'^4atatitiidè^dVtic
:, . .•---Etdllc;fixe,:ttouvetf4raI&eU«aiîbn^^ ^
AEB cft l'Equateur.
P,fohPolc:
S 3 Vf rfls^ >»> le

Zodiaque.
Z , fon Pôle.
APZ » Colure des

Solftices.
C , TEtoille donnée ,
de laquelle G T. A
Longitude » G C fa
^âtude Ibnc 'doiÀ-
nues.

^ AhegéJè ^têefiiàns Afii^ûÀùmiil$Uié

<ptlt Patigle D B N Aziniuchal par obfirrvaEÎoni.

Donc au TriangU AtBC deux cotez A C , C B « ft
i*angle CBAco^^lctneac de TangleDBN % étant
xlonncE» on trouvera Tanglefi^C A ^:qui eft.rarc lA
ou H M } lequeL étant divifé. pat 15 degtez > lé quo^
tient fera le nombre des heures requifès.

XXI IL Etàfkt cbnhuë là Hiutéur ficlaDedinaifoiX

du Soleil , ay^c l'angle Azltnuthal , trouver

. l'heure. &rEleYation duPole.^

L*arc B A complément de la hauteur du Soleil A I#
eft dgpné, A C eft auifi donne > l'angle Azimuthaleft
au$ donné > Donc^^ ^

' Câmme le Si^s de V Arc A C^

Efi émSituu^deVangle ABC %
\Ainfi le Sinuê-de AB3

£fi aià Sinus de l'angle ACB, ^Hi efi V^rc
\.^ tAon H.M y four l'heure requife.

£( pour rElevation du Pôle» voyez l'Analogie pour
trônver le<ôté BC » complément de la hauteor du
PoleCF,

TABLÉS

TABLES

DE sinus:

TANGENTES,

ET

SECANTES,

Pour un Rayon de looooooo parties,'
ET D E S

LOGARITHMES

DES S IN U S

ET DES TANGENTES,

Pour un Rayon de loooooooooo parties.

c

lo
II
li

15
14

16
li

^9

10
zi

IZ

*4

iJ
z6

z8
i^

Degrcz o

Sinus Tangent. Sécantes. Log.Sin. Log.Tting

19.09
/8.18

87.Z7

116.5^
i4y-44
174/3

z^.05^
;8.i8

«7-t7

Il^.jéllOOOOO.

141.44
174X3

Z03.6Z
Z3Z.71
Z61.80

Z03

Z3Z.71

261.80

190.%9
Il9'9%
34^-of

z^o.8^

3I5>.^«

34^07

378.1/
407.Z4
43^-33

46/.4Z

4i>4/i
jZ3.^o

//z.<8

/81.77
^io:$6

^i99S
469JO^

é^8.i3

7Z7.ZI
7/6.50
7^Si9

814.48
843/7

378.16

43^-33

100000.00

100000.00

lOOOOO.OZ

1 00^00.^4

07
100000.11
100000.16

6z looooo.:

11

1 00000. Z7
100000^3

100000.4Z

lOOOOO./I

100000.61

I00000.7Z

407.11 X 00000. 8 3

1 00000 .^j

46J.41 iooopi.08

4^4.ji 10060 1. IX
/Z3.^ 100001.37

Sf^^9
/81.78
^10.17

6}996
69%,

téy.^s tcaoo

14 XOGOOLi

7i7-*3

7/<i^-3

78/-4I

8i4.;o

843.

871

100001./3

r 00001.70
îooooii>7

looooz.oj
44

loeooa.^/

îlOQOOZ-86

100003.08

100003.31
80

60 100003.

6^100003.

6.4637Z61
6.7647/61
6.9408473

7.J088Z39
7.36681/7
7.4i7i?68i

7-4^372'/X
7./0/1181
7./4Z906/

7.06/7860
7.16Z6560
7.Z418771

6.4637161
6.7647/61
^.94oS47/

7.06/7863
7.1616564
7.1418778

7.3088148
7.3668169
7A179696

7.4^37173
7./0/1103
7-/4 1909 r

7./77^4î8f[7./77^7i/
7.6098/30 7.6098/66
7.6398160 7.6398101

7.667844/

7.^5>4I733
7.71899^^

7.741477/
7-7^47/37
7-78/9417

7.80614/8
7.81/4/07
7-^43 5^338

7.86x6^15
7.87869/3
7.89/08/4

7.9108793
7.9161 190
7.9408419

7.6678491
7.694178^

7.7x9001^

7.74*4841
7.7647610
7.78/9/08

7.8061/47
7.81/4604
7-84)^444

7.8^1673.8
7.8787077
7.89/0988

7.9x08513*
7.9161544
7.9408/84

s

89 Dcgrct,

Sinus Tancent

^o ipoooo.oo

5999999-99

Infîn

343774««7-

;8W5>9.^8 171887519

5^\999999^\^}9^}é^o
S S 99999*99^^75^^^7
5^99999^5 57^957^^

S y 99999 7 9
S^ 99999,7}
f ^[99999*66

49IloéOo
419717/7
§819709^

48

99999' S^
9999949
99999-39

^799999^9
9999917

99999.o5\l^9^9iéG

41

409999%.^!

99999-92.
99999^79
99999-63

39

Sécantes.

Infinie.

J4|774<8»
171887} 48»

i»459'î74

85945^85»
08714^^0
nX9S9o9

J4377^7i
M*J2'I57
18647773

16444080

+9110701

+1971875
38197150

54377;i«-
3iijfii97.
18647548.;

1011187J
J909%4t9

99999.47

99999.13

99991^95
99997-7^
99997'S^

99997-3^
99997 -'i A
3399996-91

16444165-
i4j;/40i-
119x838/.

11481761. ii49S99S

J$093ti0.
17188/40.

16370019

I/6z/^8.

i494^;oi
14313711

99996.^%
99996.é^
yo9999é.l9

137/074;
132118/1.

11731134

lOlllIXl

9098680

1*09345^
1^188851
1637031/

i;6l6il8^^

I494<î837

14314061

11177396.
118/4018
114/886/

1 37/1108.
131x111^
11731/16

1I177803.
118/4440^.
iî4/5|Qt

to. oooûooo

9.9999999

9-9999999
9-999999^

Lo%, S in.

Log Tatég.

InHnk.

^35369.739
13.13/1438
i3.of9i/i/

9.9999997 11.9341137
9-9999995 11.8373036
9.^999993 it.7/81111

9.9999991
9-9999999
9.9999995

11.6^117/1
11.6331831
11./810304

9-9999991
99999979
9^9999974

9'99999^9
99999964
9-P9999i9

11/361717

H.4948757

1 1.4/70909

11.411318/

j 1.3901434

11.360179^

9-99999 f 3
9-9999941
9-9999940

Ii.3}ii/ô8
11.30/8114
11.1809574

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9-99999±7^^^^i 5^390
\9-99999r9 I1.1Ï4Q451

99999i^
9-9999903
9-9999994

iyj84/3
t745i96
156955^

9-999999 s ïx^l 39 }%6%
9-9999976 Ji.yiiz5i3
9-9999966 11.1045911

999999 f 6
9-9999945
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II.085206X
11.07386/^
11.0/5x614

Aij '

5

c

Dcgrci

Sinus

Tangent.

Sccantcs.

Log. Sin.

Logi Tang.

jc

%ix,6s

871.65

100003.80

7.5408415

7.5408/84

51
31

33

3/
3^

^Pi-74
5»30.83

501.78
530.87
9S9'9^

100004.06
100004.33
100004.61

7.5/;o8i5
7.5688658
7.5811334

7.9550996
7.5688886
7.5811/34

1018.05
1047.18

585.0;
1018.14
I047-2-4

100004.85
1 0000;. 18
100Ô0/.48

7-99^9^0

8.0077867

8.0100107

7.55J1151

8.0078051
8.010044/

37
3S

iioj.H
1134.44

1076.33
110J.41
1134./1

10000/.75
100006.11
100006.44

8.031515/
8.043 J005
8.OJ47814

8.0315444
8.043/174
8.0/48054

40
4.1
42^

ii^3.J3
119^.61

1111.70

1163.61
1151.70
iitî.75

100006.77
100007.11
100007.46

8.06/7763

8.0764557
8.0865646

8.06/80/7
8.076/306
8.0865570

43
44
4/

11JO.75
1175.87
1308.56

ii;o.88
IZ79'9^
1305.07

100007.81
100008.15
ioooo8.j'7

«.0571831
8.107^1665
8.1 165161

8.0571171
8.107101/
8. 11656.34

46
47
48

1338.0/

1367.13
1356.11

1338.17
1367.16
I35^-3J

100008.56
100005.3 J
IO0OO5-7J

8.1 164710
8.13/8104
8.1445 J3i

S.1165099
8.13/8/10
8.14455/^

4J>
J4

141J.30
I4J4.35>
1483.48

I41/.4/
I4J4.J4
I483.<?4

100010.16
100010.J8

lOOOII.OI

8.1/3507/
8.1616808
8.1711804

8.I/35/I6
8.1617167
8.1713181

1/11./6

ij4i.^J

,. i;70.73

IJM.73
IJ41.83
1/70.53

3^011.4/
1000H.85
100011.34

8.1757115
8.1875848
8.1561010

8.1757616
8.1880364
8.1561//6

si

1S99'^^
1618.50
I6J7.55

1600.01
1615.11
l6j8.n

100011.80
100013.17
10001 3. 7 j

8.1040703
8.1118545
8.115/811

8.10411/^
8.1115/16
8.1156408

s^

S9

60

l6«7.o7
1716.16

174J.14

1687.31
1716.41

I74J.JI

100014.14
100014.73
ioooij,i3

8.117133J
8.i34;X^8
8.141 8//3

8.41715/3
8.1346108
8.14151XJ

1

9999 S'^i
9999^-^1
14 9999^ S^

^9 Dcgrcz

Sinus

99996.19

9999 S -9^
9999S'66

9999S'39

10110690.
5>8il75?4.3

9999^^1
99993-^9
9999 hS^

99993-^1
9999^-^9
9999^'SA

9999^-^^
99991-^1
9999^A$

i^ 99991 o^
ij 99990,6s
ix\99990.is

111^5^8^.84

}0 999^9-^1

9 999^^-99

999SS.SS
55588.11
999^7-66

55587.10
4 5558^.7 J
3 5558^.1/

999^576
999^5-^7
9558477

Tangent.

114/88^5

11085x0/
10741648
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5.6713716
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i5i68y,6o

1^1^370
1^1417,5»/
151181.36

151146.111
151011.61
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185133.13
185000.O6
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188734.36
188601.71
188465.14

188336.50
188104.70
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116/68.06

116447.11
116316.33
11610/^70

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11/564.85
11/844.71

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11/604.81
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5.5466043
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5.5464708
5.5464040
5.5463371

5.546x701
5.546x031
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10.1831145
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10.1815817
10.1816745

10.1813673
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i-53 14/75
1.9319661
15314738
1.9319808

15334873

8/5

860
861
861
863

1-5335531
1.5344584
i-53;oo3i
i-53no73
1.5360108

864
86/
866

867

1.93^/137
1.9370161

i-537fi75
1.9380151

867

868
869

870
871

871
873

874
87/
876

877
878

875
880
881

881
883
884
88/
886

Legaritb

1.9380191

1-538/157
1.5350158
1-535/151
1.54001 81

1.540/16/

1.9410141

1.541/114
1.9410080

1.941/041
1-5415556

^'9^H9^S

1.5444817
1 -54457/5

1.94/468^
1-54/9^07

^9^69^^$
i-5474337

887
8^8
885
850
851

851
853
854
85/
856

1-547513^
1.5484*30
1.5485018
1.5453500
1.5458777

1.5/03648
2..5/08/14

* 5/1 3 37;
i:.5/i8l30
1.5/13080

857

858
855

500

N

1.5/17514
1.5/317^3

i-5/37/^7
1.5/4141/

90Ô

5>oo

JV. Lûgaùth

901
901
505

90s

906

907

909
910

911
91t.

91S

i-^J47i48

1.^/^1684
1.9/^^48^

x.^j7ii8i
i.^j7^073
i.^j8o8/8

x.9j904ï^

916
917
919
919
9tO

i'9S9SlH
19S999^9
1.5^04708
X'9609^6t
x.96l^Hl

511
514

51^

517
518

530

554

i.^^l85»jj

1.5^15^55
1.^^184x7

1.5^5 5 i/J
i.5^5787«

t.5f4l/5^
15^47505
1.^^/1017
1.5^/^710
1.^^^1417

1.5^70757
1.5^7/480
i.^«8pi/7
i.^^8481^

x.5^85457
1.5^541/5
1.^^5881^

iV- Logdrith

554
55T
556
557
558

555

540
541
541
54J

1-5705465
1.5708116

1.57117/8
1.5717556
1.5712018

1.57166/6
1.5751175
1-575/856

1.5740/05
1-574/1 17

544 1-5745710

54/
546

547
548

545
5/0
5/1
5/1
5/5

1.57/4518
1.57/8511
1.576J/00
1.5768085

1.5771661
i->777i3 6
1.578180J
1.5786365
15750515

5/4
5//
5/6

5/7
5/8

5/5
560
561
561
563

564
56/
566
567

1 575/484
1.5800034
1.5804/75
1.5805115
1.5813^//

1.58x8186
1.5811711
1.58:17134

1.58317/1
1.5836163

1.5840770
1-584/173
1.5845771
158/416/

iV. \L9garith

567

568
565

570
571

571
573
574
975
576

577
57«
575

2.58/416/
1.58/87/4
1.5863158
1.5867717
1.5871151

1.5876663
1.5881128
1.588//50
1.5850046
1.5854458J

1.5858546
1-5505385
1.5507817

580 '1.551 1161
58iji.55l6650

581 1.551111/
583I.551//3/
584 1.55155/1
58/ 1.55545^1
586 1.5558765

587
588
585
550

3^-5545171
15547/65
1.55/1563
^•55/63/1

551 15560757

551
553
554
99S
996

X'996sii7
^99^9^9X
1.5575864
1.5578x51
1.5581/5/

997 ^'99969S^
999^-999110$
999h-999S6js

iooot3.ooooooQ

f*n^

looo

N.

Logarith

XOOI
lQO%
1005
1004

100 S

lOOé
ÏOO7
XOO8

lOIO

lOII

lOIX

1013
IOI4

10X6

IOI7
XOI8

1010

jx)00434X
j. 000 8^77
3.001 500^
5.ooJ73)7

|.001Ié6Z

3.001/980
3.003019/
3.003460/
3.oo389ir
3.0043114

IQXX
lOlt

X014

IQl/

3.0047/1*
3.00/180/

5.00/6054
3.0060380
3 .0064660

3.0068537
3.0073105

3.0077478
3.oo8i74x
3.008600X

3.00501/7
3.0054/05
5.005*7;^
3.oxx>3ooo!
3.0107115

1016 3.011x474

1017

IQt8

1015
IQ3$

IQJX

X031
i©34

3 .01 1/704
3.OX1553X
3.0x141/4
3.0118371

3.0X3X/87
3X)X 36757
3.9x41003
3.QI4JXO/

iV.

X034
103/
1036
1037
1038

1035
1040
1041
X041
1043

Logarith

3.014/10/
3.014^403

3X>x/3/58
3.0I/778*
3.0161574

3.oi66i//i
3.0x70333
3.0174/07
3.0x78677
3.0181843

1044
104/
xo4^

XO47
«048

104^
lO/Q
XQ/X
XO/1
lO/l

3.0x8700/
3.015x163

3.0I5./3I7
5.01554^7
3.0103613.

3.01077//

3.0111853:
3.01x6017
3.0110X/7
3.0114184

xo/4 3-0x18406
10// 3.OX3X/X/
XO/6 3.0x36635
10/7 3.0x407/0
XO/8J3. 0x448/7

xo/5
xû6o
xo6x

I

X064
106/

X066

3.ox4«y^o!
3.OX/30/5.

î-ot/71/4'

3.0x6x14/

06313.0x6/333

3.01654^ 4^

3^7349^1

3x>i77/7xl

Xo67t3.oi8x644 l

N. Logarith

X067

xa68
X065

X070
X07X

Ï071
1073
X074
107/
X076

3.018x644
3.018/711

3.0185777
3^)15383^

3^15785/

3.030154*

5*030/557
3^310043
1^3140^/
5.03x81x3

X077 5.03XXI/7
1078^ 3.0316x88
X075 30330x14
X080 3.0334x18
ïo8x 3^3381/7

Xo8x
X083
1084
X08/
X086

X087
1088

3^34xx7f
3X>346i8/
5.03/0x5^
3-05/4*^7
3.03/8x58

3.036XX5/
3X)f^6x85

X050
X05X

io85f3037^*t^
3.0574X6/

3.0378147

1051

10^3

I054{3

105/

X05^

3.0381x16

3.0386X01

.0350173

3.0354I4X
3.035810^

1057 3.040xo(<

1058 3^4060x1

X055 3*0405^77
1x0013^4x35^7

IIOO

t m

ïlOO

irioi
)iioi
1105
1104

1108
Hlo

un

ITIX

2x13
1114
JUS

iir6
UX7
ïîl8
1119

1X20

^^11

IIXJ

XX14
ïit/

1117

X|t«

XI50

fM54

Logaritk

3.0417875]
5.0411815
J.041/7JJ,
}. 0415^5^1
}.Q4}3<îi5

5'0437J/i
3.044x47^
3.044/3^8
3P445>3ij
3.04J3230

3.04/7141.
3.04éxD4&
S.o^6^9Sx
3.Q4588)'x
3.04717451

3.047^^42
3.0480/31

3.04844i«
3.0488301
3.04^1x80

3.04^50x5

^.04^^^*^
3.0/057^8
3.o/07<63
3.0JIXJIJ

3.0/1/384
yosl9^39
3.0/130^1
3.0/1^^3^

3.0/30784

3.0/3461^
3.0/384^4
3.0/4115^51

1134

II3J
X136

un
X138

3.0/4^131

3o/4?5»;9
3'OJr3785
3.0//760;
3.0/^x413

rx3^
1x40
1x41
1x41
XX43

1x44
J^i4/
1x46

1x47
rx:48

tI45?

xx/o

XX/I
Xl/1

»IJ3

11/4

II/5

IIJ7
11/8

ii/P
«1160

JI^X

II 61
ÎÏ153

l!X54

XI6/
Ï166
1167

N. Logaritk

3.0/^/137
3.0/6^048
3.0/718/6
3.0/76661
3.0/80461

3.0/84160
3.9/880//
3.0/9x846
5.o/j>/634
3.o/j»5>4X5

3.0603100
3.0606978
3.06107/3
3.06x4/1/
3.06x8193

3.06110/8
3.o6if8io

3.0619/78
4.0633334
3.0637086

.3.0640^34
3.0644/80
3.0648311'
3.06/106J
3.06//797

3.06/9/10
3.06631/9^
3.066698/
3.0670709

[167
tx68
[169
1x70
[X71

[X71
1173
1174
117/
M[76.

1x77
rx7«
tX79
[x8o
[i8x

[X8i
[183
ti84
1x8/
[186

ri87
[X88
[189
tx90
II9I

tI9i
II93
1x94
1x9/
tX96

1197
tX98

1199
[loo

3.0670709

3.0674418
3.0678x4/
3.06818/9
3.068//69

3.0689176
3.0691980
3.0696681

3.0700379
3.0704073

3.070776/

3.07x14/3
3.07X/X38
3.07x8^10

3.0711499

3.071617/
3.0719847
5-073 5 J17
3.0737183
3.0740847

3.0744/07
3.0748x64
3.07/18x8
5-O7//470
3.07/9x19

3.0761763
3.0766404
3.0770043
3.0773679
3.07773x1

3.0780941
3.0784/68

3.0788x91
3.07918x1

1100

IlOO

■m.

N.

LogariiM

1154

Logarith

-AT.

Logarith

iroi

J.075J4ÎC)

5.05151J1

1167

5.1017766

IlOl

j. 075^04;

ii3J

i. 0916670

1168

5.1051151

1105

5.0801^/6

1156

5.051018/

1165

5.1054616

1104

5.o8oéi^j

1157

5.0525^5>7

1170

5.1058057

IlOJ

5.0805870

1158
113^

5. 0517106

-

1171

5.10414//

110^

5.0813473

5.0550711

1171

5.1044871

1107

5.0817073

1140

5.0554117

1173

5.1048184

1108

5.0810^^5

1141

5.0557718

1174

5.10/1654

1105

3.08141^5

1141

5.054111^

117/

5.10//101

Il 10

5.08278/4

IM3

3-0544711

1176

5.10/8/07

iiii

30851 441

1144

5.0548104

1177

5.1061505

iiii

5.085/01^

114/

5.05/1655J

1178

5.106/508

1115

5.0858^08

1146

5.05//i8o^

1175

5.106870/

1114

5.0841187

1147

5.05/8664

1180

5.1071100

lus

5.084/7^3

1148

5.056114^

1181

3107/451

izi6

3.08455 5 tf

1145

5,056/614

1181

5.1078880

1117

5.08/1506

Il/O

5.0565100

1183

5.1081166

1118

5.08/6473

ii/i

30571x73

1184

5.108/6/0

1Z19

5.0860057

ii/i

5.057^^943

118/

5.1085051

IllO

5.0865/58

1^X3

5.057^11

1186

5.1051410

liii

5.08671/7

11/4

5.058157X

1187

5.105/78/

Iiii

5.0870711

liJJ

3.0586437

1188

5.10551/5

111}

5.087416/

11/6

5.058585^

1185

5.1101/15

1114

5.0877814

I1J7

305553X3

1150

5.110/857

111/

5.0881561

11/8

5.0556806

1151

5.1105161

iiié

5.088450/

l^S9

5*10001/7

1151

5.111161/

1117

5.0888446

1160

5.100570/

1153

3.iir/58x

1118

5.0851584

1161

5.10071/1

J154

5.1115543

111^

5. 085//! 5

Ï161

5. 1010/54

J15X

5.H11658

1150

5.08550/1

1165

5.1014055

1156

5.1 1160/0

un

5.0501/80

1164

3.1017471

1157

5.1x15400

Iljl

5.0506107

Ii6/

5.101050/

1158

3.ii5i74<^

ïiJÎ

5.0505651

izéé

5.1014337

1155

5.1136051;

1134

5.05151/*

1167

5.1017766

150c

^1I594?3

N iîj 130a

I300

N.

1501

IJOJ

1304
130J

Lâgarith

141775
14^110

149444
i/i77<?

1506

IJ07
1308
130^
1310

13IX
1311

X515
IÎI4

13 16

I5I7;

1318
131^

1310 ;

I3II
I3II;
IJI3
IJI4

131^

15*7 3
1318

X5*9
1330

Ï551
1551
1555
>554

1/9432'
I^17J^
1^^077

171715

17^017

ï7935«
181^47

18/9/4
1^9^/7

191SS9
I9/8j«
1991/4
101448

10/73^

lopoiS
11231/
11//98
118880
iiii/^

**/45/
118709
131981
13/1/0
138/Kf

1417»!
14/041
148501

AT.

354
55f
55^
557
558

559

540
541
541
545

544
54/
54^
547
548

549
5/0
5/1
5/1
5/5

5/4
5//
5/<î
5/7
5/8

5/9
3^0
3tfi
3(51
5^5

5^4
5<^7

Logarhh

5.11/1XJ8

511/4815
3.xi/8o^j

3.11^1314
3.11^4/^1

3.11^780^
3.1 171048
3.1 174188

3.1177/1/
3. j 180760

51185995
5.1187113

3.11504/î
3.11^3^76

3.lî5><899

3.x 5001 ip
5.1305558
5-X506/J3
hi ^097^7
3.1311578

3.151^187
51519595
3.1511/97
3.131/798
3.1318598

3.1331x5/
5155/589
3.1 5 38/81

J.134Ï771
h^i^^9S9

3.1348144
3.13/131^
3.X3/4/07I
3.i3/7(g8/

X567
X3é8
X5^9
X570
1371

JV* Logarith

1571
1575

X574
157/
1376

1577
1578
X579
X580
1381

X581
1585

X

138/
1386

5845

X587
X588

1589
X390
1391

159^1
Ï595
1594
159/
159^^

1597
1598

X

1400

5995

3.13/7^8/

5.X36086I

3.1364034
3.1367106

5157057/

51575/41
3.Ï 37670/

5.x 379867
3.1583017
3.X386184

5.1589559
3.13^1491
5.i59/<î45
5.1598791
3.140x557

3.140/080
3.1408111
.14I1361
3.1414498
3.1417631

3.14107^/
3.141389/
3.1417011
3.X450148
3.1435171

3.1436351
3.X439/11
3.X441618

5 •144/741
3.14488/4

3.I4/X5<54
5.X4//071
.X4/8177
M 461180

1400

1400

N. LçgAmh

140Z
1401
1403
1404
X40;

1406

1407
1408
1405»

141 c

I4II
1411
1413
I4I4
141/

X4lé

1417
I4I«
141^

X410

14"
14"
X413
I4M
141;

142^
1417
X418

1430

I4ÎÏ

1451

I4J4

3.14^4381
14^7480
î 1470/77
3.1475^71
3.147^763

314758/3
3.1481^1
3.148^0x7
3.148^110
3.14^11^1

3.145/170

5i45«J47
3.1/01411

3.1/04454
31/07/^4

3.i/io^3J
3.i/iJ^58
3.i/U7^t
3.ijip8i4
3.1/1x883

3.1/^/541

3.1/1855^

3.1/31049

.1/3/100

.1/38145

3.X/4115/
3.1/44140
3-1/47181
3.1//0311
3.i//33^o

3.i//é3^
3-1//5430
3.1/614^1
31 /'g/451

iNT.

Logariih

1434
143/
I43<î
1437
1438

1435
1440
1441
1441
1443

1444
144/
144^
1447
1448

1445
14/0
14/1
14/1
14/3

14/4
*4//
14/é

14/7
14/8

14/5
1460
14^1
1462
1463

14^4

14^^.
14^7

1/^/451
1/^8/19

1/74/^8
1/77/85

1/80608

1/83^1/
1/86640
15^965^
1/51663

1/5/671
1/58678
1601683
160468/
1607686

X610684
16x3680

I 61 6674
1619666
I6ii6s6

I 61/644
X618630
163x6x4
1634/5^
1^37/7/

i^40//5
i^43/»5
I 64^/0 t
1^45474
1^/1445

i^//4n

X6/8376
166x340
I 66430 I

iv;

Logarith

X467
1468
X465

X470
1471

3.1664301

x6«7i6x
X670H8

1^7317^
X 676x17

1471
1473
1474
147/
X476

1477
1478
Ï475
1480
148X

1481
1483
1484
148/
X486

1487
1488
1485
1450
I45X

•1^75078
•I681017

.X68457/
.X687510
x 650864

165380/

X 656744
16996%%
17016x7

1708481
171x411
1714335
17x716/
1710188

X7131X0

X 716015
X 718547

173x863
173477^

i45«p^^37^88
3.x 740/58
3x743/06
3.X7464XI
5.174531^

M53
1454
145/
1456

1457
1458
1455

I f 00

N iiij

3.X7/111I
517//118

5.i7/8ox^

ri76o9l j

1500

I5Ô0

IJOI

IJO3
IJO4

ISO S

IJ06
I/o?
1/08
JS09
r/io

ijii
ijii
1/.13
1/14
i£i;

1/16

1/18
I/I5>
1/20

Logarith

17^5807

1769590

1771478
I77;36;

IJ22
ITI5
1/^4
IJl/

1/26

1/^7

1/28

I/25I
1x30

• 1/51

IJ33
ÏJ34

17782/0
1781132
1784013
1786852
1785765?

175264/
Hp/fi8

17^838^
I 8012/5
I 804126

1806552
18058/6
1812718
181//78
181 8436

1821252
182414^
1826555
18258/0
1832658

183//4/
1838350

I 841134
184407;
I 846514

18457/2
18/2/88
18//421
lgj8i/4

AT.

Logaritif

1X3^

IJ3;
1/36

1/37
1/38

Î.I8/82J4

3.1861084
3. 1863511
3.1866735

yiS69S6^

1/39

1/40

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3.1872386
3.X87/207
3.1878026
3.1880844
3.18836/5

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3.1886473
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3.18545^03
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3.1500/14

3.1503317
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3.1508517
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3.1514/10

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3.1520056
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5.15413^7
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JV. Logarith

156-7
1/68

1/65

1/70
I/71

1/71
1/73
1/74
1/7/
1/76

1/77
1/78
1/75»
1/80
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1/82
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3.15/0650
3.15/3461
3.15/^115
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3.1961761

5.15^4/1/
3.1567187
3.1570047
3.1571806
3.157//61

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1581070
1583821
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3.100/765
3.2008/0/
3.2011235

3.2013571
3.2016701

3.ioi543i
3.10111/8
3.1014883
3.1017607
3.1030325

3.1033045
3.103/768
3.103848/
3-1 041100

1600

i6oo

N. Logarith

i6oi
i6oi

1604
ï6os

létOé

1607
1608
1609

\6lQ

1611
l6ii

1^14
I61S

I6lr6

161
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1619
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161 f

1616
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1619
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163/
1636
1637
1638

163^
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1648

164^
16/0
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16 s 9
1^60
1661
1661
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1664
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1171107
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118/3//
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1667
1668
1665
1670
1671

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3.11153/6
3.1111560
3.1114/63
3.111716/
3.1115764

1671
1673
1674
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3.1131363
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3.1137///
3.1140148
3.1141740

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16É3
1684
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1687
1688
1685
1650
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1651
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1657
1658

3.11/8160
3.1160841
3.1163411

3.116/55^
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3.11711/1
3,1173714
3.1176156
3.1178867
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3.1184004
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3.1151657
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3.1156818
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1701
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3.1317144

31319790

3.13*1-35/
3.1314875

3.1317411
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3.1381571
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1754
175/
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1757
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175^
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1741
174*

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3.147481J
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3.1484637
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3.1456874
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1803
1804
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3.1674064
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3.1651794
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3.17051x6
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x«67'j

x868

1865

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1871
1873

1874
187/
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1877
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1875
1880
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1.1780673
1781961

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1900

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X901

1901

1904
190 S

J906
1907
190^
1909
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5.181 réo7
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5.18171x0
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5.1810554

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1558

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5.18650x4
5.1871156
5.1873x38

5.187x778
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5.18801XX
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5.1884718

5.1886565
5.1885156
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5.1858118

5.1500346

5.1501x75
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5.150514^
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5.155141X
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5-2'^5J83X
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1567
1568
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1570
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197/
157^

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1578
1575
1580
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1584
158X
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1587
1588
1585
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1555
1554
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15>57
1558
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1000

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5.1558044
15401x1
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1544661
1546866

1549065
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2000 f

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1001
1003
1004
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1006
2007
1008
1009
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201 1
2011
2013
2014
201/

2016
2017
2018

XOJ9

2020

2021
2021
2023
2024
202;

2026
2027
2028

XO%9

2030

2031

2032

2054

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501330^

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2034
203/
2036
2037
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2045
20/0
20/ 1
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2-0/4
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10/6
10/7
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1060
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119657
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136/63
138671
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2067
1068
2065

1070
2071

3-31/540/
3.31///0/
3.31/760/

3-31/^703
3.3161801

2071
2073
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207/
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2077
2078
2075
2080
2081

2082
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2087
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3-3i^/?93
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3.315^384
3.3201463
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1167
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1170
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3.35/8/8?
5-55^o/?3
3-35<?i/?6
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1175
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1183
1184
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3.54x63x3

5.54x8301
5.34x0x77
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1203
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120J

iio6
1107
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111}
1114
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111^

1117

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3-34478/1
3-344^814
34JI77*
3-34J37J7

h34SS^9t

3J4/7^J7
y34S96is
ÎJ4<^IJ73
3.34^3x30

•5.3 46/486
3-34^7441
3-34^^3^/
3.3471348
3-3475300

347;i/î-

3477101

3479ÎJ*
3481101

548504^

5484^^^
54$6>4i|
34I8887
54^0831!

3ti34
113/
1136
1137
1138

»-^$9

1140
1141
1141
«'»43

1144
»i4/
ii4i

1147
1148

114^
11/0
il/l
11/1
11/3

iiT4
ai//
11/6
11/7
11/8

11/^
1160
ii6x
il6i
1163

Lêgdfith

11643
I116/I5
ii66>3

54^0832.
34^177/
34^4718
34^6660
34^8601

3/00/41
3/01480

3/0441^
3/063/6
3/08193

3/10118
3/11163
3/14098
3/16031
33'i7^<3

$yi9hs
3/1181/

3/157TJ
3XiJ^84

3/*7«"^

3X^^/3^
3J3i4^/
3X3335X
3J3/3I*
3X3713^

3/39KJ1
5/41084
3/45006
3/44^1^
3/4^846

3/487^4
3//0681I

5/J*/H
5^4/1/1

1167
1168
1169

1170
1171

1171
1173
1174
117/
1176

1*77
1178

^^79
1180
1181

1181
1183

1184

Lûgdfith

5.3//6450

3 3//834/
3.3/^01/9
3.3/^1171

3.3/^4083
y$S^5994r
3-3/^7^0/
3.3/<558i4
3-33'7i7i3

3.3/73^30
3-3J7//37
3-3J77443
3.5/7^348
3.3J811/5

3.3/831/^
5,3/8/0/9
3-3/8^^^1
118/3.3/88861
1186 3.3/90761

ii87'3. 3/91^61
1188 3-3T>4/^o

1189
1190
1191

1191
1193
1194
119/
119^

ti97
1198

1299

2300

3-3J5>i?4/8
3-5J3>83//
3.36001/1

3.3601146
5.3604041

3-5^/^54
3.5607817
3.3609719

3.5^11^10
5 3^ï3/oo
3.56I/390
5.5617178

1300

1300

N. Logarith

1501
1501
1303
1304
130J

1308
1305
1310

1311
1311

1314

3.36110^-3;

3.3611939
3.36x481/
3.3616709

1306 3-3^i8j93
13073-3^3047^
3.36313/8
33^3413^
3.3636J10

hi^37999
3.3^35^878
3.36417;^
3-3H3<^34

x}i6
1317
1318
1319
1310

1311
1311
1313
1314
131J

1316
1317
1318
1319
1330

1331
1331
1333
l334

3.3647386
3.3649160

3.3^/1134
3-3<î/3oo7
3.36J4880

3.3^/^7/1
3.36/8611
3.3660491
3.3661361
3.3664150

1.3666097
3-366796^
3669^30
3.367169/
3-3^73JJ5^

3.3677x8/

3.3679147
3.3681008

7\r. Logarith

1334
133J
1336
1337
1338

3.3681008
3.3681869
3.3684718
3.3686/87
3.368844/

3.3690301
3-3^9ii/i?
3.3694014
3-3^^/869

133^
1340
1341
1341
I343l3-3^977i3

i344 3-3^5>9/7^
134/3-3701418
134^(3-3703180

134713-370/131
1348.3.3706981

1349
13/0

13/1
13/1
13/3

13/4
*3//
13/6

13/7
13/8

i3/5>
1360
1361
1361
1363

1364
156/
1366
1367

3.3708830
3.3710679
3.3711/K^
3-3714373
3.3716119

3.371806/
3.3719909

3-37117/3
3-37i3/5>6
3371/438

3.3717179
3.3719110
3.3730960
3.3731799
3.3734637

3.373647/
Î-37383H|
3.3740147

3.37419831

N.

1367
1368
1369
1370
1371

1371
1373
1374
137/
1376

1377
1378
1379
1380
1381

1381
1383
1384
138/
1386

Logarith

3-3741983
3-3743817
3-374/6/1

3-3747483
3.3749316

3.37/1147
3-37/1977
3.37/4807
3-37/6636
3-37/8464

3.3760191
3.3761118
3-3763944
3-376/770
3-3 767/94

3.3769418

3.3771140
3.3773061
3.3774884
3.3776704

1387
1388

1389
1390
1391

1391
1393
1394
139/
2-596

1397
1398
1399

1400

3.3778/14
3-3780343
3.3781Ï61
3-3783979
3.378/796

3.3787611
3.3789417
3.3791 141
3.37930//
3.3794868

3.3796680
3.3798491
3.3800301
3v38oiiit

Z4OO

2.400

N.

1401

1401 ;
1403

1404 ;
^40/

Logatith

8o;73o
807/38

805134;
8111/1

240^

2407 :

2408

240^;

2410 ;

241 I
2412 ;
2413

i4i4i

2416
2417
2418
241^

2420!

2421

2422:

2423

2424:

^■42./

241e

2428 ;
24IP;

M50

241 1
2431
1453 3
X434

814761

818368

810170

81J971
8i3775
81/J7J
8^7375
815171

830P65
83176^

834/^)
8363/5?
8381/4

85i>5>48
841741

845;34
84/316

847117

8485^08
8/0658
8/1487

8j4t7J
8/6063

8/78/0
8/5636
861411
863106

TV. Logarith

2-454
^43/
243^
^437
1438

^Ai9
1440

2-441
1442

1443

1444
144/
144^
^447
2.448

3.3881011
3.3881785
3.3884/6/
3.3886340
3.3888114

i445>
14/0
14/1
14/2
14/3

14/^3

14;/

14/6

14/7
14/8

24J5»
1460
1461
14^1
1463

1464

X4^/
1466

2-4^7

3.3863106
3-38<J4^yo
3.3866773
3.3868///
3-3870337

3.3871118
3.3873858
3.387/678
3-38774x7

3.3885S88
3851661

5-3853433
3-385/IÔ/

3-385657;

3858746

3-35'oo/i/
3.3501184
3-3^040/1
3-35>ci/8i5

5-35>07/8/

119091$^
3.35»iUi6
3.3511880
5.3514644

3.3516407
$.^91^169
}'l9i99n

N:

1467
1468
1465
1470
1471

1471

*475
1474
H7;
1476

2.477
H78
^475
1480
1481

1481
2.485
1484
148;
i486

1487
1488
1485
1450
14^1

i4^i
14^3
2 4M
i4^/
i4^6

'. ) •

^

1-457
M^8
*45>^

1/00

Logarith
J51160Z

39Z)4S^
3^1/11 î
5516570
3528727

35>3048/
5932.241
59339^7
55>5/7;2'
55^37/06

5539260
5941013
594176/
5 944/ ï 7
j 9^6149
— ^ ■■ *' »»
5948018
5949767
59/X/I6
}9Syx6^
y9SS9ll

J 9/67/8

}9S^SQ^
5960145

I96l99i

5965757

i96s4^(?
J 967113.
5968564
597079/
597i44(^.

597418;
i97S9i-^
5977^6^

59794

^50*

4QP

Si

XJOO

N* Lêgérith

tjoi
%SOs

i/07

M^«4^0g

hî99iS^$
3'i99}%7S

199S007
33996737

3399^^(7
3.4000196

i/ïj 3Aooi9%s
3tfiHj.400/jJo

tsto

t/*4

ÎI111421

J.4007I06

).4ooSS|i
J.4019//7
3.401 iiSz
3.40I4P9J

3.40ï/7a«

3-40I74/I
3.401^173
3.40*08^3
3.401Ù14;

5-40*4333
3.4o^60S^
3-401777Ï
3.40*M«g

3^0jIA0J

3.40|ip*i
3^4014^57
3.40^^5/*

^/54

i/3é
1/J7
1/38

^S39
1/40
^J4I
1/41
»/4J

Lâgdriih

3.4038066
3.403^7^0
5-404i45>i
3.404310/
5-4044^1^

3.4046617

3.40483 J7

3.40/0047

340/17//
3.40/3464

1/44
1/4/
1/4^
1/47
i/48

1/4^
1//0
1//1
1//1

3-40//I7I
3.40/^«7«
3.40/8/84
3.406018^1
3.4061^^4

3.40636^8
3.406/401
3.406710/
3.4068807
i//3|3-4070/q8

1//4
1///
!//<
iJ/7
1//^

1/60
1/61
1/61
1/63

3.40:1^*0^
3-4073^0^
3.407/^08
3.4077307
3.407^00/

^//^3. 4080703
3.4081400
3.40840^6
3.408/7^1
3.40874J86

i/64|3ufo89i8Q

3.40^08.74
3. 40^1 f 67
3>405>4i/5

1/6/
1/66

1/67
1/68
1/6^
1/70
1/71

1/71
1/73
1/74
1/7/
î/76

Logarith

3A094^S9
3 409 S 9 so
3.40:^7641

3-40^^331
3.4101011

1/77
1/78

1/7^
1/80
i/8i

1/81
1/83
1/84
1/8/
1/86

3.4101710I
3.41043^81
3.410608/

3.4107771
3.4^0^4/^

3.41 II 144
3.41x181^
3.4114/13
3.41161^7
3.4117880

1/87
1/88
i/85>
i/5»o
^S9l

3^tl9S6i
3.4111144
3.4lii5>î/
3.411460/
3.411618/

1/^1

i/3>3
l/i>4
1/^/
1/56

i/5>7
i/5>8

^S99

1600

3.41 175^64
3.4115643
3.4131310
3.41 313^58
3-4i34<î74

5.413^3/0
5.413801/
5.4135700
34141374
3.4143047

3. 41.4471 J
3-4î4^35i
3-fi48o63
^4I4573^

1600

l^OO

A7 Xo^arith

l6oj
i6oi

1603

x604
1^0/

1606
1607
2.^08
1609
l6io

1614

161%
t6l9
16 10

1^11

1^X1
X6X4

J.41JI404

3.4IJ4741
j.4ij^4io

j. 41/8077

J.4IJ^744
3.4161410
J.4I6J076
3.4164741
3.41^^40;

3.4168065

3.416^31

3.4i7i3i>4
3.41730/6
3.4174717

J -41 7^ 3 77
3.4I7«037

3.417^^56
3.41813//
3. 41 8301 3

3.4ï«4670
3.41863x7

3-4ï«7^83
3.4185638

t6x/ 3.4151293

t6x6
167 X
26x8

X630

3.4x51547
3.4154601
3.4ï5<^x/4

i6i5 3-4ï^75>oé

34159//7

3.4x01x08
3.4x0x8/5
34x04705
3.4x061/8

iST. |iLif£4riri&

X634
163/
X636
X637
X638:

3.4^061/8

3.4x07806

3-410^4/4
3.41x1101
3.4x1x748

1^35
X640
X641
x64x
X643

1^44
164/
X646

1^47
X648

1645 3.4x308x0

3.41143M
34x16035
34X17<584
3.4x15318

34x1057*

34XXX6Ï4

3.4XX41/7
34XX/858

3-4117/3^
3.4XX5180

16/0
x6/i
16/2
X6/3

x6/4
16//
X6sé
X6/7
X6/8

3413x4/5
34134057

3.4137371

3.4135005
3^414064/
34141181
3.4143516
3.414///0

»^/5
1660
x66i
i66x
X663

1664
166/
1666
1667

34x471*3
34148816

3-41/044P
3.41/1080
3.41/3:^11

3.41//541
3-41/6571
541/8601

34160130

livr.

Lûgarith

1667
1668
X665
X670

X671

34H^î3^
34x61 8/1

3^x634«4
3 4x6/1 1|

3.4x6673^

1671
1673
X674
167/
X676

X677
1678

1^7^
x68o

3-4i68}6/
3.41655^9
3.4x71614

3-4175 13^
3 417486 1[

3417^4*4

3.4178*06

3.4x7^717
3418134^

x68l 3.4x8x568

x68x

x6«3
X684
x68/
x686

3.4184/88
3.4x86x07
341878X/

34x85441
3.4151060

X687
x688
X685
X650
X651

1691

X653
1654
165/
1696

3 4i5i<77
34x541^?
3-41^/^08

3-41^7/M
3.4155137

343007/1
3.430x364

3.430357^
3430//88

3 -4 3071^^

1657
X658

1655

X700

o

3.4308805
343104x5
3.431x0x5
3-4313638

1700!

lyoo

iVr. Logarith

1701
4701
170J

17P+
Z70j>

1706
1707
1768
1709
1710

1711
i7ii
t7i5
1714
X7Ï/

1716
1717
1718

171^

1710

17*1
1711
1713
4714
^7M

171^
1717
1718
1719
a.750

47JI
1751
1755
17H

5.431/146
J.43168/}
3.4318460
3.43x00^7
3.4511673

3.43x5178

5.4514885
5.45x^487
3.45180^0
3.43i5>6^3

5-45511^/
5.45518^7
J.45J445»8
5.455605Ï8
5.4557^58

5.455^15^8
5.45408516
5.43414^4
5 .454405»!
5-454X68^

5.454718/
5.4548881
5.45/0476
5,45/1071
5-45X366/

3-4î/Ti;8
5.45/68/ï

5-45/8444
5.456005/
5.4561616

5.4365x17
3.4564807
5.456655^6
5-4567^8/

1754
175;
X756

1757
1758

175^
1740
1741
1741
1745

1744
174/
1746

1747
1748

1745»
17/0
17/1

17/1
17/5

17/4
17//
17/6

17/7
17/8

17/^
1760
1761
1761
1765

1764
176/
1766

1767

Logarith

î-45675>8/

5-4365>/75
5.4371161

3.457x748
5-45745 54

5'457/5>io
5.4577/06
5-457^050
5.4380674
5.43811/8

5.4585841
7-458/415

5.438700/
5-4588/87
5.455JOI67

5.455>i747
5. 45 5> 5 517
5-45^4^06
5.45^6484
5.45^8062

5.45^^635?
5.4401 116
5.44017^2
5,4404568
5-440/^45

5.4407/17
5.44050^1
5.4410664

5.4411157
5.44i58o5>

3.441/580
5.44169/I
5.4418/11

3.44x00^1

1767
X768

176^

1770
177Ï

1771
1775
1774
177/
1776

1777
1778

177^
X780
X781

1781
1785
1784
178/

1786
■ ■ ■■ »■
1787
1788
1785?

i75>o
17^1

17^1
17^5
17M
175»/
17^6

17^7
175>8

17^^

1800

Lûganth

44100^1
4411 661
4415x50

44i475>8
441656/

44175^51
44194^^

445106/

4451650

44541P/

Mi SI 59
4457511
445888/

4440448
444x010

4445/71

44466^1
44481/1
44 4^811

.44/1570
.44/1^18
44/448/
44/6041
.44/7/5>8
^ —

44/^1/4
446070^
4461164
4465818
446/571

4466^1/

4468477

4470015

5.447 1/80

2800

2.8oo

N.

iSoi
^8o^
1805
1804
180/

i8o6
1807
1808
280^
1810

x8ii
1811
i8ij
2814
i8ij

z%i6
18x7
i8i8
i8i^
zSxo

x8ii
0.812
x8i3
2814
28xj

281^
1817
i8i8
ziX9
1830

X851
1.832

i»34

Logarith

3.4473 131
3.4474^81

3-447^2'3i
3-4477780

3-4^^33^^

3.4480877
3.4481424

3.4483j>7i
3.448JJI7
3.44870^3

3.4488^08
3.445>oij3

j. ^9 16 97
3.44^3241
3.44P4784

3,44^632^
3.44i?7868
3.44^5410
3.4joo^ji
3.4/024^1

3.4/04031
3-4;o/j70
3.4J07I05>
3.4/08^47
3 .4/101 84

3.4/11722
3-4JI3M8
3 -4/147^4
3.4/1^325?

3.4/178^4

h^5^9l99
V4/i05>32-i
1.4/2146^1

3-4/^3^^

2834
283/
283e
2837
2838

Logarith

3.4/23^5^8

3-4J1JJ31
3.4/27062
3-4Ji8/^3
3.4/30124

2835
2840
2841
2842
1843

2844
284/
2846
2847
2848

284^
28/0
28/1
28/2
28/3

28/4
28//
28/6
28/7
28/8

28/^
1860
286X
2862
2863

2864
286/
x866
2867

l-4J3i^i4
3-4/33183

3,4/3471 i
3.4/36241
3-4/377^^

3-4J3^i^6
3.4/40823
3-4/4134^
3 -4X43 87/
3-4/4J40P

3.4/46924
5 -4/4844^
3-4/4^*71
3-4/;i4^J
3.4//3018

3.4J/4;40
3»4Jj6o6i
3-4J/7/82
3.4//9I02
3.4/60622

34/62142
3.4/6366Q

3-4/6^17^
i -^566696
3.4/6811^

3 -4X65^7 30
}.4/7ï*46
3.4/717^ ^
3-4X74X77

N. Logdritb

2867
1868
2869
2870
2871

2872
2873
1874
287/
2876

2877
2878

2875>
2880
288X

3-4X74177
3-4X7X7^1
3-4X77*0/
3-4x78819"
3-4x80332

3.4x81844
3-4X833X6
3.4X84868
3.4X86378
3-4x87889

3-4X893^^
3-4x^0908

3.4x^2417
3-4X535>3LX
34X^X433

2882
2885

3-4x56940
3-4X58446

i884|3. 4X599X3
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AU LECTEUR.

COmme il cft important d'avoir*. des
Tables trcs-correftes , & qu'il eft diffi-
cile d'en avoir d'exa£tcs fans y prendre un
foin particulier j je me fuis efforcé à vous
lesdonner,MoN cher Lecteur, dans
la dernière exactitude. Pour cette fin je les
ay fait imprimer fur celles d'Ulacq , qui ont
cté imprimées à la Haye en Tannée i66^. &
qui pafTcnt pour cftre des plus corredes : &c
je les ay ait fait corriger fur celles du même
Ulacq , imprimées à Amjfterdam en l'année
1685. qui partent pour eftre e;ncore plus cor-
redes que les précédentes, afin de pouvoir
connoîpre les fautes qui y feroient , lôrfqu'il
fe rencontreroit quelque différence entre les
chiffres de l'une & .de J/aùtre de ces deux
différentes éditions , ce qjni m'a fait décou-^
vrir àcs fautes qu'on ne trouvera point icy.
Et pour une plus grande perfedion , aupa-
ravant que de faire imprimer ces Tables ,
j'ay préîu avec beaucoup de foin celles
d'Ulacq , ayant corrigé les Sinus fur les Ta-
bles de Pitifcus in folio , U les Logarithmes

auLecteur.'
fut câix d'Henry Bhggs auifi in folio y ce
qui m*afaic découYrir quelques; fauces efTeft--
tielles , &: plufieurs autres de moindre con«
fequence , qu^on avoir négligées dans tou-
tes les redirions , & qu'on ne uouvera point
dans cellê-cy. Ainû Ton peut s'afTurér d^a*
voir icy des Tables autant exaâcs qu il eft
pofliWe*^